The development and current status of luminescent solar concentrators is reviewed. These solar concentrators generally consist of transparent polymer sheets doped with luminescent species; presently mainly organic dye molecules are used as luminescent species, however semiconductor nanocrystals are gaining interest. Direct and diffuse incident sunlight is absorbed by the luminescent species and emitted at red- shifted wavelengths with high quantum efficiency. Optimum design ensures that a large fraction of emitted light is trapped in the sheet, which travels to the edges where it can be collected by one or more mono- or bifacial solar cells, with minimum losses due to absorption in the sheet and re-absorption by the luminescent species. Optimized luminescent solar concentrators are predicted to offer potentially lower cost per unit of power compared to conventional solar cells. Various design and material aspects will be discussed using thermodynamic and ray-trace modeling techniques and recent experimental results are presented. (C) 2012 Elsevier Ltd. All rights reserved.