This the title of a new paper by Atila Abdulkadiroglu and Tayfun Sonmez which was presented at the 2010 Econometric Society World Congress in Shanghai.
This survey cover both one-sided matching and two-sided matching. In Section 2 they introduce and briefly go over some of the key results in two-sided matching model by Gale and Shapley (1962). In Section 3 they introduce the "housing market" model by Shapley and Scarf (1974) as well as a number of more recent one-sided matching models, some of which are closely related to two-sided matching models. In Section 4 they present the recent developments in School Choice and in Section 5 they present the recent developments in Kidney Exchange.