The eigenvalues of non-hermitian matrices with very few nonzero entries do not exhibit the same behaviour as their hermitian counterpart. In this talk I will expose these differences, then present a few results on the extremal eigenvalues and the log-characteristic polynomial of two models of sparse matrices, namely directed Erdos-Rényi graphs with constant average degree, and sums of random permutations. This is based on various works with Ludovic Stephan, Gaultier Lambert and Yizhe Zhu.