The road leading to this dissertation was not free from stress or problems, but many people have helped making the journey fulfilling and entertaining. First and Foremost, I want to thank my advisor, Tim McKay, for the training and the guidance. I had no previous experience in astronomy or astrophysics, but Tim took me on without hesitation. Over the years, I learned a great deal from his words and deeds: how to do research, how to write and speak about research results, and how to establish fruitful collaborations. I also feel lucky that Tim helped me raising awareness about work-life balance and being practical while being a perfectionist.I have been working with Chris Miller a lot since 2013. In the past a couple of years, he treated me as one of his own students and taught me many research skills without any reservation. He was keen on making me to pursue extra research, collaboration and observation opportunities. I would have missed many of them if it wasn't him.I learned a lot about cosmology theories and simulations from the weekly meetings organized by Gus and Dragan. Gus is alway pressing me for my latest proposals and paper drafts, and offered many insightful feedbacks. Dave and Greg mentored my research with the DES collaboration, and helped to make sure that I communicate with people about my work. Michigan postdocs Joerg and Jeeseon supervised me when I was a junior graduate student. Michigan alumni Adam and Tomasz offered many helpful dicussions while they were here.The bonds with the DES collaboration and the XCS collaboration (the XMM Cluster Survey) have benefitted me enormously. The feedbacks from the DES cluster working group, the DES galaxy evolution working group and the XCS collaboration are critical in shaping my DES and XCS projects. Many collaborators have generously provided their code and catalogs, or patiently answered my questions about data and simulations. More than twenty people have commented on my paper drafts at different stages of preparation. The telephone discussions within the two collaborations are always inspiring and motivating. This section would become too long if I list the people that have helped on various issues, but at least let me thank Kathy Romer here for supervising my participation in both the DES and the XCS collaborations.My friends have helped to make the past five years fruitful and unforgettable: Scott,ii Tom, Paul and Arina, Ping, Zhao, Mijin, Arya and many others. I especially want to thank Jia Xu for taking care of me after an exercise accident. I am grateful that my family has always stood with me. My brother across the Pacific ocean helped me staying connected to different sides of life. My parents were understanding, cheerful, and eagerly helpful. I've become interested in mathematical and physical science since childhood. However, being a female, it took some extra courage to push it through. My parents were firm that women deserve any kinds of excellence and happiness with any kinds of career choice. This dissertation is dedicated to my mother an...