More than 40 years ago, Erdos asked to determine the maximum possible number of edges in a $k$-uniform hypergraph on n vertices with no matching of size $t$ (i.e., with no $t$ disjoint edges). Although this is one of the most basic problem on hypergraphs, progress on Erdos' question remained elusive. In addition to being important in its own right, this problem has several interesting applications. In this talk we present a solution of Erdos' question for $t < n/(3k^2$). This improves upon the best previously known range $t = O (n/k3)$, which dates back to the 1970's.Joint work with H. Huang and P. Loh.