The extent to which grain boundaries (GBs) in polycrystalline materials may be detrimental, benign, or even beneficial is explored with numerical simulations in two dimensions. We focus on the effects of GB recombination in Cu(In,Ga)Se2 (CIGS) solar cells and its effects on solar-cell performance. The simulations predict that (1) for device effciency exceeding 17%, the effective GB recombination velocity must be less than 104 cm/s; (2) grain boundaries within the space-charge region (SCR) lower the open-circuit voltage, whereas the short-circuit current is reduced by grain boundaries in the bulk material; and (3) horizontal GBs are relatively benign unless they are located in the SCR. Modifications to the electronic structure near grain boundaries show that charge-induced band-bending at grain boundaries will most likely have a negative effect on device performance, whereas a down-shift in the valence-band energy at the grain surface can effectively passivate the GBs and reduce the effective recombination velocity. For the models considered, GBs generally have a deleterious effect on effciency, and GBs alone can not explain the apparent superiority of polycrystalline over single-crystalline CIGS materials.