The prospects for cost-effective flat plate (non-concentrator) solar cells based on III-V compound semiconductors (e.g., GaAs, InP, AlAs, and their alloys) are reviewed. Solar cells made in III-V materials are expensive, but outperform solar cells in every other materials system. The relatively high cost of compound semiconductor wafers necessitates a means to eliminate their use as substrates for epitaial growth of conventional III-V solar cells. There are several approaches to this end, including thin-film solar cells on low-cost, dissimilar substrates such as glass, ceramics, and metal sheets; III-V solar cells epitaxially grown on silicon wafers; film transfer (‘epitaxial lift off’) techniques that allow re-use of the seeding substrate; and assembled arrays of small III-V solar cells on low-cost substrates. Grain boundary effects in polycrystalline III-V films can severely degrade solar cell performance, and impede the application of established thin-film technologies, as developed for amorphous silicon and II-VI semiconductor photovoltaics, to III-V semiconductor-based solar cells. The nearly fifty years of effort in developing thin-film III-V solar cells has underscored the difficulty of achieving large-grain sizes and/or low recombination grain boundaries in polycrystalline films of III-V semiconductors.