http://docs.embed.ly/docs/native

embedly-responsive-iframe-host.js

window.addEventListener('message', function(e) {
  var data;
  try {
    data = JSON.parse(e.data);
  } catch (e) {
    return false;
  }

  if (data.context !== 'iframe.resize') {
    return false;
  }

  var iframe = document.querySelector('iframe[src="' + data.src + '"]');

  if (!iframe) {
    return false;
  }
 
  var div = iframe.parentNode;
  
  // Update the responsive div.
  div.style.paddingBottom = ((data.height/iframe.offsetWidth)*100).toPrecision(4) + '%'
});