Recent advances in molecular organic photovoltaics (OPVs) have shown 10% power conversion efficiency (PCE) for single-junction cells, which put them in direct competition with PVs based on amorphous silicon. Incorporation of plasmonic nanostructures for light trapping in these thin-film devices offers an attractive solution to realize higher-efficiency OPVs with PCE >> 10%. This article reviews recent progress on plasmonic-enhanced OPV devices using metallic nanoparticles, and one-dimensional (1D) and two-dimensional (2D) patterned periodic nanostructures. We discuss the benefits of using various plasmonic nanostructures for broad-band, polarization-insensitive and angle-independent absorption enhancement, and their integration with one or two electrode(s) of an OPV device.