A few people have asked me to help understand what's going on in Ukraine, considering that I lived there and I have made Ukrainian geopolitics the area of my graduate study. Go to the bottom for the tl;dr.
Upon independence, one of the first laws passed in Ukraine basically gave a blanket pardon to anyone arrested by the Soviet regime, as it was practically impossible to tell who had been jailed for political reasons and who had not. Another law established that those who held political positions had a kind of amnesty where they could not be tried for past crimes. As a result, many gangsters and others of the criminal class entered the political arena.
At this time, everything was in a fevered state of chaos. Though there was no violent regime change, the entire political, economic, and social system had been thrown up in the air. Part of this was a transition to a market economy wherein many formerly state-owned properties and facilities were privatized, often in back-room deals well below any actual market value. As a result, a very small group of people (called the oligarchs) got extremely rich. This pattern was repeated across the entire former Soviet Union.
In 2004, the "Orange Revolution" took place, which was spearheaded by the one-two punch of Viktor Yushchenko, who became president, and Yulia Tymoshenko, who became prime minister. Their primary opposition was Viktor Yanukovich and his Party of Regions. The Oranges picked up a lot of support in the West, where both Yushchenko and Tymoshenko were based, and showed themselves to be a major challenge to the very powerful Party of Regions. During the 2004 election cycle, Yushchenko was poisoned with acid, which disfigured his face; he did not drop out of the race. On election day, the votes came in favor of Yanukovich, but the Oranges cried foul, accusing the Party of Regions of vote tampering. This is when the "revolution" happened, which ended up sweeping Yushchenko and Tymoshenko into office, but at a cost: the constitution was amended, taking much of the power away from the office of the president and giving it to the parliament. As a result of this compromise, many quickly became disillusioned with the Oranges (because without expansive presidential powers, Yushchenko really couldn't make good on any of the promises of the "revolution") and political infighting within the coalition contributed to the failure of the Orange movement. The administration was racked with problems, most importantly that the economy didn't grow nearly as much as everyone had hoped and promised, and Tymoshchenko made a shady deal for a discount on Russian gas. What happened there was Russia, who is by far Ukraine's number one source for oil and gas, shut off the pipes to Ukraine in winter over a price dispute. The Russian-government-owned gas company wanted more money for gas and was freezing out Ukrainians. In response, Tymoshenko—stepping outside the limits of her powers as prime minister—signed a deal with Russia to fix gas prices in exchange for an extended lease of the port of Sebastopol in Crimea to Russia's Black Sea Fleet. After Yanukovich's 2010 election, Tymoshenko was promptly jailed for her actions, though many saw this more as a politically-motivated arrest rather than for any criminal activity (I bring this up to show that this deal is no more shady than any of the ones Yanukovich makes in the next section).
The Euromaidan protests from November 2013 to February 2014 began in reaction to president Viktor Yanukovich's decision to back out of talks with the EU, which would have set up some trade agreements and get Ukraine closer to possible future EU membership. Very quickly—within a week, basically—the scope of the protests expanded to more generally be about the widespread and rampant corruption of Yanukovich's government and the Party of Regions. While no government of independent Ukraine has been completely free of corruption, Yanukovich really took it to the next level, essentially bankrupting the country for the enrichment of himself, his oligarch backers, and his circle of friends, called the Family. So instead of engaging in talks with the EU, which would have placed a number of demands on Ukraine, including releasing Tymoshenko from prison and opening up Ukraine to more EU imports (which probably would have had an adverse effect on Ukraine's economy, as Ukraine doesn't really have much to export to keep the trade balance level), Yanukovich took a deal from Putin that included $15 billion in cash to Ukraine. From a realpolitik perspective, taking the Russian cash deal was the only option that made sense, but that is before taking into account the aforementioned corruption and a host of geopolitical implications.
The protests were mainly peaceful and continued to grow throughout the winter, and continued to garner western media attention. All of this was a thorn in Yanukovich's side and in January, Yanukovich pushed through a number of illegal/unconstitutional laws that prohibited the rights of free speech and assembly, specifically targeting the Euromaidan protesters, authorizing use of force against them. The presence of fascists among the protesters was the primary justification for the laws. Though extreme right-wing groups like Svoboda were involved in the protest, and in many cases were the instigators in some of the more violent demonstrations and the tearing down of statues of Lenin for example, the numbers of fascists are extremely low in Ukraine in general and on the Euromaidan. The anti-assembly laws though changed the nature of the protest, as it became about survival against a regime who decided it better to eliminate the protesters outright rather than have to deal with them. These anti-assembly laws also came on the heels of a Russian promise for more money if Yanukovich "took care of" the protesters and reestablished a stable regime.
The backlash against the anti-assembly laws was huge and international. The numbers of protesters surged and they overtook a number of government buildings and a number of Yanukovich's oligarch backers pulled their support. Meanwhile, the police and special forces used live ammunition on the protesters and there were many instances of protesters disappearing, being tortured, and then either reappearing in hospitals at the point of death or never reappearing at all. After a number of days of murderous terror, in a special session of parliament, the prime minister, Azarov, said that he would resign, and the parliament repealed all of the January 16th laws. They had a parley with the three leaders of the opposition—Klitchko, Tyanhibok, and Yatsenyuk—and attempted to negotiate a deal. The negotiations to end the protest failed as the opposition would not relent until all of its demands were met. Shortly after the Olympics finished, a provisional deal was struck where a special election would be held by December 2014, but that timetable was quickly moved up to May 25 as the protesters continued to seize government offices and buildings, forcing Yanukovich to leave the capital, upon which the opposition declared that Yanukovich had been deposed. Around this time, Tymoshenko was also released from prison. Other decisions as a result of the opposition's success include a return to the 2004 constitution and repealing the law that Yanukovich passed which made Russia a second official language of Ukraine.
The provisional government had only a few days to get itself up and running before Putin sent a cadre of troops into Crimea, to the Black Sea Fleet base in Sebastopol. This is where things get tricky as a bunch of conflicting reports surfaced right after each other. And here I'd note that it is still muddy, trying to determine which news sources are reporting actual facts, which are editorializing, and which are inventing facts. But from what I can tell, Putin's plan looks extremely similar to what he tried in Georgia in 2008: bring in troops to "protect" ethnic Russians in other states, distribute Russian passports, and to provoke an attack by local authorities. Keep in mind that Russia's incursion is entirely without provocation and many russophone Ukrainians have signed a petition telling Putin that they don't need any "protection" and that the Ukrainian government isn't persecuting them.
But Ukraine is not Georgia, for a couple of major reasons. First is the stakes: Ukraine is much more important to Russia's geopolitical long game than Georgia (more on that below). Second is international law: in 1994, Ukraine signed a deal with the US, the UK, and Russia giving up its nukes in exchange for military protection. This was a necessity because Ukraine doesn't have a real army. Though military service is compulsory for young men in Ukraine unless you go to university, the military has no money, no equipment, and not much to do. One report I read stated that there are only about 500 active duty-ready troops in the entirety of Ukraine's armed forces. Third is NATO, which became a factor almost immediately after Russian troops hit the ground in Crimea, as Latvia and Lithuania called an emergency NATO meeting to decide on a course of action.
What hasn't happened in Crimea, at least not yet anyway, is a war. This is largely because Ukrainian forces, despite Russia's taunting, have not fired a shot. They've simply let the Russian troops into the country, in clear violation of international law. But unlike Georgia who started shooting, Ukraine's provisional central government is waiting on the rest of the world. At the same time though, Crimea's prime minister has essentially declared Crimean secession from Ukraine, though the central government claims that Crimea's prime minister has no legitimate authority. While Crimea is the only Ukrainian oblast (state) with a majority of Russian ethnics and has a relatively high level of autonomy, it is still subject to the central government in Kyiv. It is also the only Ukrainian state to have a large "indigenous" Muslim population, the Crimean Tatars, who are allied with the central government.
Various reports have come in regarding ultimatums: either Ukraine does such-and-such or Russia will launch a full-scale invasion or Crimea will declare its independence. This is where geopolitical posturing and the role of the media come into play in a major way: since these reports are almost all in conflict with each other, there are all kinds of questions regarding what's a legal claim or not, and different media outlets are all reporting sensationalized versions of these stories, each steeped in their own particular ideologies, getting at the "truth" of what's happening is extremely hard for an outside, particularly western, observer. Part of that is because western media do not understand the complexity of the situation and all its moving parts and have a vested interest in painting Russia in the worst possible light (as NBC's coverage of the Olympics made quite clear). Be extremely suspicious of any news source that claims that one group is responsible for everything, or that there is one cause to the whole situation. Western, particularly American, media is unwilling or unable to convey that complexity, in part I think because they do not believe that western/American audiences can handle learning about a political system that is radically different from the two-sides-of-the-same-coin political system in the US.
There are fascist parties active in Ukraine (like Svoboda). There is an active communist party (UKP). There is an active socialist party (SPU). There are a number of neoliberal parties and a number of social democrat parties. There are parties that revolve around a particular politician (like Tymoshenko's party). In fact, there are over 120 political parties in Ukraine, with most arranged into political coalitions called blocs in order to pool resources and votes together to create temporary politically expedient alliances. Each of these parties has its own agenda, and each wants a cut of the pie in the provisional political atmosphere that Ukraine finds itself in now. And because things are so chaotic and there is a weak center, each of these parties—or at least the larger, more active, and more ideologically-driven ones—is ramping up their agitation. And all of this while a foreign power is occupying part of the country. It's rather impossible to tell right now how this is all going to shake down. What it's really going to come down to is the next step Russia takes, whether that's getting Crimea to secede, starting shooting people, or pulling out. NATO, the US, the UK, and the UN (which, unless it kicks Russia out of the security council, can't do anything at all) can only react (outside of making what amount to be empty threats). For better or worse, it's Russia's move, and everyone knows it.
Ukraine's position is a tenuous one, on the margins of both the EU and the emergent Eurasian Customs Union, a Russian-led response to the EU. Its position in relation to either side though couldn't be more different. The EU, as it stands right now, does not need Ukrainian membership. In fact, the EU probably doesn't even want Ukraine right now anyway. They will, however, need new markets to export to in the event that the EU can survive this global depression relatively unscathed (which remains to be seen). What the EU wants right now is what those talks in November were going to be about: a Europe-friendly Ukraine to essentially continue to be both a buffer against and a thorn in the side of Russia, a country the EU wants to remain relatively weak but still willing to sell their sweet, sweet oil and gas to Euro markets.
Russia on the other hand is playing an entirely different game. Positioning itself to be on the economic upswing, Putin's administration is trying to piece together a world where Russia is a major player once again. This is manifested in their Olympic display and in the strong central administration under Putin, which fosters a conservative nationalism, rooted in tradition, but a tradition that sees itself as both a major imperial power and a post-war super power. One of the keys to this plan is the ECU, a visa-free coalition a la the EU but one where it's clear that there's an economic and political center. In essence, it's an early Soviet model in terms of administration, but opposite in its ideology: in this regard, Putin is closer to reestablishing the Russian Empire rather than the USSR. In the greater Eurasian region, Russia is doing a great job of recruiting China to its side so far, building gas and oil pipelines in abundance.
Of course, Russia's plan also contains a socio-cultural element, one that condemns the west for its hypocrisy and its neoliberal guiding ideology. It accuses the west of abandoning morality, caring more about profits than people, and not practicing what they preach, especially when it concerns America's military "interventions" and meddling in the internal affairs of other sovereign entities. This is why, when the west cried foul at Putin's Crimean invasion, he could essentially say, "hey, I'm just doing the exact same thing you've been doing all over the world for decades" and be correct, not claiming a moral high ground per se, but certainly knocking the US off its high horse. This then is a direct challenge to US hegemony and is the most interesting part: though many Ukrainian leftists staunchly oppose the Russian invasion of Ukraine, they also staunchly oppose western meddling because to them, it's the same old imperialism, just coming from two different places. Problem is, their own government is in an interim state and there's no domestic army to protect them, which is why groups like the UKP are organizing their own militias (in this case, to take care of the fascists at home first, then mobilizing against the imperialists).
Cast in this light, the struggle for Ukraine, at least from the left, is a struggle against neocolonialism from the west and outright imperial colonialism from the east. It is a struggle against the flows of global capital that have bankrupted Ukraine both in money and in people (for much of the past two and a half decades, for example, more people were leaving Ukraine for work elsewhere than being born in Ukraine). Though the leftist faction of Ukrainian politics is noticeable, it is still a minority voice however. For most Ukrainians, the meaning of the Euromaidan protest, the upcoming new government, and how the Crimean situation is handled and pans out is essentially rooted in the right for Ukrainians to determine Ukraine's future, free from meddling from both Russia and the west, to be a player in its own right, not just a pawn or a powerless buffer state.