We consider {0,1}-matrices. For matrices A and B, we say A contains B as a configuration if there is a submatrix of A that is a column and row permutation of B. For instance, if A and B are incidence matrices of graphs G and H respectively, then A contains B as a configuration if and only if G contains H as a subgraph. In this talk, we study some extremal problems for matrices and hypergraphs (set systems).