There is an increasing worldwide demand for high energy density batteries. In recent years, rechargeable Li-ion batteries have become important power sources, and their performance gains are driving the adoption of electrical vehicles (EV) as viable alternatives to combustion engines. The exploration of new Li-ion battery materials is an important focus of materials scientists and computational physicists and chemists throughout the world. The practical applications of Li-ion batteries and emerging alternatives may not be limited to portable electronic devices and circumventing hurdles that include range anxiety and safety among others, to their widespread adoption in EV applications in the future requires new electrode materials and a fuller understanding of how the materials and the electrolyte chemistries behave. Since this field is advancing rapidly and attracting an increasing number of researchers, it is crucial to summarise the current progress and the key scientific challenges related to Li-ion batteries from theoretical point of view. Computational prediction of ideal compounds is the focus of several large consortia, and a leading methodology in designing materials and electrolytes optimized for function, including those for Li-ion batteries. In this Perspective, we review the key aspects of Li-ion batteries from theoretical perspectives: the working principles of Li-ion batteries, the cathodes, anodes, and electrolyte solutions that are the current state of the art, and future research directions for advanced Li-ion batteries based on computational materials and electrolyte design.