The response of a thin liquid film that is subjected to an electric field is of fundamental scientific interest and technological importance. Indeed, liquid films subjected to electric fields have recently been used to form desirable patterns in soft lithography and occur widely in precision thin-film coating applications where unwanted fields can mar product quality. The method of choice in determining the response of a liquid film to an applied electric field has heretofore been linear stability analysis (LSA). While LSA has proven extremely useful in obtaining the critical field strength and the critical wavenumber for the onset of instability, LSA cannot account for nonlinear effects that are often prevalent in applications. We address this deficiency of LSA and previous studies by attacking the problem with a combination of a weakly nonlinear analysis and a full-blown nonlinear analysis based on large scale numerical simulations using the finite element method (FEM). The results of the weakly nonlinear analysis are shown to be extremely valuable in developing insights and predictive heuristics into the underlying physics. The accuracy of the numerical solutions is verified by comparison to those of the weakly nonlinear analysis when the interface deformations are moderate. Situations in which extremely large interface deformations arise, e.g. in applications in which polymer microstructures are patterned without resists, exposure, development, and etching, are demonstrated to require the full power of the FEM analysis.