(This is work in progress with Dominic Dotterrer and Larry Guth.) In a graph, the girth is the length of the smallest cycle. How large the girth can be for a graph on n vertices and m edges is a very well studied problem in combinatorics. More generally, in a d-dimensional simplicial complex, we define the d-systole to be the smallest nonempty collection of closed d-dimensional faces whose union has no boundary, and we measure the size of a systole in terms of volume, i.e. the number of faces. It is natural to ask what is the largest possible d-systole for a simplicial complex on n vertices with m top-dimensional faces. We show the existence of simplicial complexes with large systoles using random simplicial complexes with modifications, and we also require some new results on estimating the number of triangulated surfaces on a given number of vertices. On the other hand, we show that the systoles can not be much larger than this, so these results are essentially optimal. In the higher-dimensional setting, there are surprising contrasts with the classical graph theoretic picture, and in particular the systoles can be quite large.