Luminescent Solar Concentrators (LSCs) offer a way of making Photovoltaic (PV) systems more attractive through reduced energy costs, the possibility of application in cloudy regions, and improved building integration. LSCs collect light over a large area and concentrate it, both spatially and spectrally, onto solar cells at the edges of the device, such that the total cell area required to generate a specific power is reduced. Since the solar cells constitute the more expensive component in the system, this leads to cost reductions. Unlike conventional geometric concentrators, LSCs do not require solar tracking and can collect diffuse as well as direct sunlight. The current research challenges lie in increasing the efficiency of the LSC and extending it to larger areas to make it commercially viable. In this chapter, the authors outline the mode of operation of the LSC, with particular regard to cost considerations and device geometry. They then review recent approaches aiming to increase device efficiency and, finally, introduce their versatile raytrace approach to modelling the LSC. The model is utilised here to investigate tapered LSC designs and rationalise the optimal geometry and configuration for planar LSCs.