Frictions are a potentially important feature of many two-sided settings, for example, in the marriage market. My dissertation develops and estimates two-sided search and matching models and uses them to assess the importance of frictions in explaining observed marriage patterns. In the models, unmatched individuals search for long-term partners. Opportunities to meet potential partners arrive over time at uncertain intervals. Individuals are of different observable discrete types (e.g., gender and race/ethnicity) and types vary in their proportions within the population. Types may also differ in their type-pair specific utilities of marrying and their likelihood of meeting certain types of potential spouses. The first chapter in my dissertation proposes a new identification approach to separately estimate type-specific preferences and opportunities. I implement the technique to understand the marital patterns of racial and ethnic groups in the United States and to analyze the reasons for a high degree of same-type marriages. The second chapter theoretically analyzes the implications of the assumption that people prefer same-type partners. I show that frameworks with and without search frictions deliver different insights about the effects of group size on matching outcomes.