In strong electromagnetic fields, new plasma phenomena and applications emerge, whose modeling requires analytical theories and numerical schemes that I will develop in this thesis. Based on my new results of the classical plasma model, the role of strong magnetic fields during laser-plasma interactions can now be understood. Moreover, based my new quantum electrodynamics (QED) models for plasmas, it is now possible to understand strong-field QED effects in astrophysical environments and test them in laboratory settings.First and foremost, I would like to extend thanks to my advisors Nathaniel J. Fisch and Hong Qin. I am deeply indebted to Nat and Hong, not only for advising and guiding me in research and teaching, but also for encouraging me to explore other branches of physics. Their open-mindedness enabled me to find synergy between quantum field theory and plasma physics, and do research on topics that are unimaginable anywhere else in the world. I am forever thankful for the excellent role models they have provided as successful physicists, professors, and mentors. I am deeply grateful for my collaborators Qing Jia, who carried out simulations of magnetized laser pulse compression, and Jianyuan Xiao, who coded and performed simulations of scalar-QED plasmas. It has been a privilege to work with such a talented peer group. Discussions with Qing, Jianyuan, as well as Matthew Edwards, Kenan Qu, Sebastian Meuren, and Wolf Malkin have always been inspiring and fruitful.For this dissertation, I would like to acknowledge my readers, Ilya Dodin and Edward Startsev, for their time and constructive feedbacks. I am thankful to members of my thesis committee: Ilya Dodin, Allan Reiman and Julia Mikhailova for their time, guidance, and insightful questions.Many people have read the work presented in this dissertation and generously provided valuable comments. I would like to extend my sincere thanks to