Since its development in the 1970s, the rechargeable alkali-ion battery has proven to be a truly transformative technology, providing portable energy storage for devices ranging from small portable electronics to sizable electric vehicles. Here, we present a review of modern theoretical and computational approaches to the study and design of rechargeable alkali-ion battery materials. Starting from fundamental thermodynamics and kinetics phenomenological equations, we rigorously derive the theoretical relationships for key battery properties, such as voltage, capacity, alkali diffusivity, and other electrochemically relevant computable quantities. We then present an overview of computational techniques for the study of rechargeable alkali-ion battery materials, followed by a critical review of the literature applying these techniques to yield crucial insights into battery operation and performance. Finally, we provide perspectives on outstanding challenges and opportunities in the theory and computation of rechargeable alkali-ion battery materials.