For a sequence A of integers, S(A) denotes the collection of partial sums of A. About forty years ago, Erdos and Folkman made the following conjecture: Let A be an infinite sequence of integers with density at least $Cn^{1/2}$ (i.e., A contains at least $Cn^{1/2}$ numbers between $1$ and n for every larger n), then S(A) contains an infinite arithmetic progression. Partial results have been obtained by Erdos (1962), Folkman (1966), Hegyvari (2000), Luczak-Schoen (2000). Together with Szemeredi, we have recently proved the conjecture. In this talk, I plan to survey this development.