This review summarizes the optical and electrical models of bulk heterojunction (BHJ) polymer solar cells (PSCs) and numerically simulates and analyzes the performance of the PSCs. A complete simulation of a conventional BHJ device based on the polymer P3HT is presented and results are compared with the experimental data. Key factors affecting the device performance, including the photo absorption, quantum efficiency, short-circuit current, fill factor, and open-circuit voltage of the device, are analyzed and summarized. Simulations on inverted, semitransparent, and large-area PSCs are performed and findings are compared with experimental results. Simulations reveal the effects of optical spacer layers, different thicknesses, carrier mobilities, light intensities, contact barriers, effective bandgaps, recombination coefficients, and energy-level bending on the quantum efficiency, short-circuit current, fill factor, and open-circuit voltage of the PSCs. Differences between conventional and inverted geometry, opacity and semitransparency, and small and large-area PSCs are discussed based on the simulations. A power conversion efficiency of 11.0% is predicted for the PSC based on P3HT. Results suggest the need to further reduce the series resistance in large-area PSCs. (C) 2014 Elsevier B.V. All rights reserved.