since the foundational results of chung-graham-wilson on quasirandom graphs over 20 years ago, here has been a lot of effort by many researchers to extend the theory to hypergraphs. i will present some of this history, and then describe our recent results that provide such a generalization in some cases. one key new aspect in the theory is a systematic study of hypergraph eigenvalues first introduced by friedman and wigderson. this leads to the study of various extremal questions on hypergraphs, for example, spectral tur an problems and spectral packing problems. this is joint work with peter keevash and john lenz.