The cost of photovoltaic power can be reduced with organic solar concentrators. These are planar waveguides with a thin-film organic coating on the face and inorganic solar cells attached to the edges. Light is absorbed by the coating and reemitted into waveguide modes for collection by the solar cells. We report single- and tandem-waveguide organic solar concentrators with quantum efficiencies exceeding 50% and projected power conversion efficiencies as high as 6.8%. The exploitation of near-field energy transfer, solid-state solvation, and phosphorescence enables 10-fold increases in the power obtained from photovoltaic cells, without the need for solar tracking.