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.