Szemeredi’s regularity lemma says that any graph can be approximated by a finite grid of quasirandom graphs. A series of results show that various model theoretic tameness notions - NIP, stable, and distal - guarantee various additional properties of the approximating graphs. Once we generalize to hypergraphs - that is, to k-ary relations with k>2 - the situation becomes more complicated. Without assuming prior knowledge of graph or hypergraph regularity, we will discuss the generalizations to tame versions of weak hypergraph regularity, and our recent result with Chernikov giving a generalization of the NIP case to full hypergraph regularity using the notion of $NIP_k$ hypergraphs.