Let A be a finite set of integers. The sum set, A+A, is the set of pairwise sums from A and the product set, AA, is the set of pairwise products. Erdos and Szemeredi conjectured that either the sum set or the product set should be large, |A+A|+|AA| is (almost) quadratic in |A| for any subset of integers. This problem (and some of its variants) became one of the central problems in additive combinatorics.In this talk we will survey the related works and present some recent results.