This dissertation consists of three chapters covering applications within Matching Theory. In the first chapter, we study the decentralized college admissions in the Kingdom of Saudi Arabia (KSA), where students submit their applications to each college separately, and colleges use a ranking based on weighted centralized test scores. Unlike the other decentralized college admissions, a student is not allowed to keep two offers on hand at the same for more than two days. Colleges give their acceptance decisions at different times and may finalize their admissions before the others. Moreover, offers are usually expiring offers. Motivated by these features, we formalize the college admissions in KSA as a game where colleges may give acceptance decisions simultaneously or sequentially. When there are two colleges, we show that the equilibrium outcomes of both simultaneous and sequential moves are fair. We propose a methodology to compare games by their wastefulness, and we show that the sequential move game outperforms the simultaneous move game in terms of eliminating waste. We find that allowing colleges to determine the number of students to accept strategically will result in fair and non-wasteful equilibrium outcomes under both simultaneous and sequential move games. In the second chapter, which is joint work with Umut Dur and William Phan, we formulate the allocation of hajj quotas as a market design problem. Hajj is an essential pillar of Islam in which every Muslim needs to fulfill once in their life whenever possible. The Organization of Islamic Cooperation (OIC) allocates hajj slots using a quota system to the member countries. The Western countries that are not OIC members consume the residual slots. Applicants with dual citizenship can simultaneously apply for hajj slots in both OIC and Western countries. This situation may hurt the applicants without dual citizenship from OIC countries. Moreover, it might lead OIC member countries to act strategically by lowering the applicants' priorities with dual citizenship. Motivated by this observation, we propose a sequential allocation procedure in which the Western countries allocate their slots first. We show that this allocation procedure maximizes total assignments and removes incentives for applicants and countries from being strategic players. Lastly, we propose two alternative procedures to transfer unused slots to OIC applicants to decrease their waiting time.In the third chapter, we study the effects of precedence order (i.e., the order in which different types of seats are filled) on college admission under the Texas House Bill 588 (popularly known as the Top 10% Law). The Top 10% Law required any public institution to automatically admit any student who graduated in the top 10% from a Texas high school. After receiving numerous applications from the top 10% students, the University of Texas at Austin limited the number of students it will admit via the Top 10% Law. The university usually admits the top 10% students for the reserved seats for them and then admits the rest of the applicants based on merit ranking. We evaluate the effects of changing the admission order. Using administrative data, we estimate college preferences over students and then analyze the effect of different admission orders in our counterfactual analysis. Our analysis quantifies the importance of processing order in college admission. Despite the increase in the top 10% students' admission, changing admission order has an adverse effect on Hispanic students. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]