Image Quilting can be used to synthesize a large texture from a tiny texture; it was coined in Efros 2001, which introduced the idea of a cutting a minimum cost path through a tile to make the seams less discernable. ("Image Transfer" is also discussed in this paper, which is less interesting to me.)
Wang Tiles were popularized in Cohen 2003. These make it possible to apply image quilting over an infinite region, by baking out a small set of orientable tiles. (They can also be used for generating maze-like structures, which is somewhat orthogonal to the image quilting stuff.)
Wang Tiles can also be used to generate aperioidic tilings of blue noise (or point samples), and they can even be applied in a recursive manner, which allows for infinite zoom; see Kopf 2006, as well as this excellent post from @joesfer.
Any image can be made be tileable using a simple blending technique. Scroll down to Part 2 of Paul Bourke's write-up about Tiling Textures on the Plane.
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