The understanding of lightning strike damage mechanisms of fiber-reinforced polymer matrix composites (PMCs) is of great significance in the design and development of lightning strike protection (LSP) systems for aircrafts and wind turbine blades. The recent extensive experimental studies on lightning strike response of fiber-reinforced PMCs have provided us qualitative understanding on various lightning strike damage mechanisms (e.g., delamination and ablation). However, results from those studies are unable to fully identify parameters of both lightning strike and composite materials that are affecting the lightning strike response. Theoretical analysis and effective predictive models are needed to carefully identify those parameters and provide design and optimization guidance for LSP. At this time, the available models are quite limited and still far from manurity. In this paper, we provide an overview of our recent efforts on the development of predictive models of lightning strike on composite materials, which include the determination of lightning strike boundary conditions (e.g., heat flux and current density) for composite materials and modeling of the degradation and thermal damage in composites subjected to lightning strikes. In addition, we assess limitations and provide future recommendations for this research topic.