This talk discusses on the behavior of fiber reinforced polymer matrix composites subjected to electric fields ranging from the low-magnitude fields encountered in damage sensing applications to the extremely high-magnitude fields occurring during lightning strikes. First, electrical characterization methods for carbon fiber reinforced polymer (CFRP) composites subjected to a variety of electric fields will be presented. Extensive experimental studies of the electrical response and damage sensing capabilities of continuous carbon fiber reinforced and textile composites subjected to low-velocity impact will be discussed. The effective conducting thickness concept and a methodology for building finite element (FE) models of electrically anisotropic CFRP materials will be discussed along with its integration with quasi-static FE models for predicting and sensing impact-induced delamination in laminated composites. The second part of the talk will focus on the behavior of composites under extreme electromagnetic fields that arise during lightning strikes. Physics-based models that describe electric and thermal fields and include surface interaction between a lightning channel and a composite structure will be introduced. The models include: (i) spatial and temporal evolution of the lightning channel as a function of the electric current waveform; (ii) temporary and spatially non-uniform heat flux generated at the composite structure; (iii) nonlinear transient heat transfer problem formulation for layered anisotropic composites that accounts for temperature-dependent material properties, a moving boundary of the expanding lightning channel, and phase transition moving boundary associated with instantaneous material removal due to sublimation. Computational algorithms for the multi-layer composite laminates will be discussed.