Luminescent solar concentrators (LSCs) generally consist of transparent polymer sheets doped with luminescent species. Incident sunlight is absorbed by the luminescent species and emitted with high quantum efficiency, such that emitted light is trapped in the sheet and travels to the edges where it can be collected by solar cells. LSCs offer potentially lower cost per Wp. This paper reviews results mainly obtained within the framework of the Fullspectrum project. Two modeling approaches are presented, i.e., a thermodynamic and a ray-trace one, as well as experimental results, with a focus on LSC stability.