Light water reactors operated under supercritical pressure conditions have been selected as one of the promising future reactor concepts to be studied by the Generation IV International Forum. Whereas the steam cycle of such reactors can be derived from modem fossil fired power plants, the reactor itself, and in particular the reactor core, still need to be developed. Different core design concepts shall be described here to outline the strategy. A first option for near future applications is a pressurized water reactor with $380^{circ}C$ core exit temperature, having a closed primary loop and achieving 2% pts. higher net efficiency and 24% higher specific turbine power than latest pressurized water reactors. More efficiency and turbine power can be gained from core exit temperatures around $500^{circ}C$, which require a multi step heat up process in the core with intermediate coolant mixing, achieving up to 44% net efficiency. The paper summarizes different core and assembly design approaches which have been studied recently for such High Performance Light Water Reactors.