High conversion reactor (HCR) design methods have been used at the Technical University of Braunschweig (TUBS) with the technological support of Kraftwerk Union (KWU). The present state and objectives of this cooperation between KWU and TUBS in the field of HCRs have been described using existing design models and current activities aimed at further development and validation of the codes. The hard physical and thermal-hydraulic boundary conditions of pressurized water reactor (PWR) cores with a high degree of fuel utilization result from the tight packing of the HCR fuel rods and the high fissionable plutonium content of the fuel. In terms of design, the problem will be solved with rod bundles whose fuel rods are adjusted by helical spacers to the proposed small rod pitches. These HCR properties require novel computational models for neutron physics, thermal hydraulics, and fuel rod design. By means of a survey of the codes, the analytical procedure for present-day HCR core design is presented. The design programs are currently under intensive development, as design tools with a solid, scientific foundation and with essential parameters that are widely valid and are required for a promising optimization of the HCR core. Design results and a survey of future HCR developments are given. In this connection, the reoptimization of the PWR core in the direction of an HCR is considered a fascinating scientific task, with respect to both economic and safety aspects.