There are several notions of dimension for non-commutative algebraic varieties (= certain triangulated categories). I will review two of them - the Rouquier dimension, based on generation time, and the Serre dimension, based on iterations of the Serre functor. I will talk on their properties, both established and conjectural, and compare these with what one would expect from a dimension. I will demonstrate a series of examples where dimension is known and use it to motivate some conjectures. This talk is based on a joint work with Valery Lunts.

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