The article gives brief view about the achievements of Lloyd Shapley and Alvin Roth, whohave been awarded in 2012 the Nobel Prize in Economics «for the theory of stable allocations and the practice of market design». After the winners’ short biography we discuss the main results of their work. The first part addresses Gale and Shapley pioneering paper, in which they were the first to consider the problem of an equilibrium in a two-sided market without money-transfers: this result became the basis for an important part of economics – the matching theory. After that the most important Roth’s theoretical results on Gale and Shapley model are discussed. Finally, several modifications of the classical model, made by Roth and his coauthors, are reviewed, those modifications provided theoretical basis for analysis of real world matching markets.