The U.S. Department of Energy initiative Generation IV aim is to produce an entire nuclear energy production system with next-generation features for certification before 2030. A Generation IV-capable system must have superior sustainability, safety and reliability, and economic cost advantages in comparison with third generation light water reactors (LWRs). A gas core reactor (GCR) with magnetohydrodynamic (MHD) power converter and cascading power cycle forms the basis for a Generation IV concept that is expected to set the upper performance limits in sustainability and power conversion efficiency among all existing and proposed fission powered systems. A gaseous core reactor delivering thousands of megawatt fission power acts as the heat source for a high-temperature MHD power converter. A uranium tetrafluoride fuel mix, with ~95% mol fraction helium gas, provides a stable working fluid for the primary MHD Brayton cycle. The hot working fluid exiting a topping cycle MHD generator has sufficient heat to drive a conventional helium Brayton cycle with 35% thermal efficiency as well as a superheated steam Rankine cycle, with up to 40% efficiency, which recovers the waste heat from the intermediate Brayton cycle. A combined cycle efficiency of close to 70% can be achieved with only a modest MHD topping cycle efficiency. The high-temperature direct-energy conversion capability of an MHD dynamo combined with an already sophisticated steam-powered turbine industry knowledge base allows the cascading cycle design to achieve breakthrough first-law energy efficiencies previously unheard of in the nuclear power industry. Although simple in concept, the gas core reactor design has not achieved the state of technological maturity that established high-temperature gas-cooled reactors and high-temperature molten salt core reactors have pioneered. However, the GCR-MHD concept has considerable promise; for example, like molten salt reactors the fuel is continuously cycled, allowing high burnup, continuous burning of actinides, and hence greatly improved fuel utilization. The fuel inventory is two orders of magnitude lower than LWRs of comparable power output, and fissile plutonium production is likewise lower than in spent LWR fuel. Besides these features, specific GCR-MHD design challenges such as fission enhanced gas conductivity of the MHD partially ionized gas, GCR safety issues and related engineering problems are discussed.