This thesis consists of four chapters. The first chapter explains the relevance of the research that has been undertaken and it contains an overview of this research for a general audience. The second chapter studies a multi-unit assignment with endogenous quotas in a dichotomous preference domain. The main conclusion I obtain is that pseudo-market mechanisms perform poorly in this type of environment.The third and fourth chapters use matching theory to understand segregation in matching environments ranging from integrating kidney exchanges platforms to the increase in interracial marriages after the popularization of online dating platforms. In both Chapters, using different formulations, I show under which conditions social integration can be obtained.