A hole is an induced cycle with at least four vertices. A hole is odd (even) if its length is odd (even). Holes play a central role in the structure of graphs. For example, hole-free graphs (i.e. chordal graphs) can be decomposed by clique cutsets into cliques. Two natural generalizations of chordal graphs are odd-hole-free and even-hole-free graphs. It is known that graphs in these two classes have their chromatic numbers bounded by a function of their clique numbers. We will discuss a number of open problems on the structure of odd-hole-free and even-hole-free graphs. In particular, we will discuss a conjecture by Cameron, Chaplick and the author that the tree width of an even-hole-free graph is bounded by a function of its clique number.