An overview of the fundamentals, the optimization strategies, and specific optical designs of concentrators for concentrated photovoltaic (CPV) systems is given. Several designs of secondary optical element (SOE) were compared with respect to their CAP and the achievable photocurrent densities. When using silicone on glass (SOG) Fresnel lens primary optical element (POE), special attention has to be given to the temperature effects of this POE type. It is shown how these effects can be minimized. Concentrator optics for CPV modules are lowest-cost high-volume optical elements. This puts very strong constraints on the parameter space of theoretically feasible optical designs. The field of concentrator optics for CPV is still emerging and it is only recent that very important feedback from the operation of CPV modules in high volumes can be gained. Many possible design variants the most promising will be selected and incorporated in the next generation CPV module designs.