Sasakian geometry is the odd-dimensional cousin of Kahler geometry. Although the two are very closely related, there are some interesting differences. I will give an introduction to Sasakian, and in particular Sasaki-Einstein, geometry, and review some of the developments in this subject over the last few years. In particular I’ll cover explicit constructions, toric Sasakian geometry, and obstructions. Some of these results also provide new insights into Kahler geometry – for example, I’ll describe very simple new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.

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