A nuclear reactor system that, in one embodiment, utilizes natural circulation to circulate a primary coolant in a single-phase through a reactor core and a heat exchange sub-system. The heat exchange subsystem is located outside of the nuclear reactor pressure vessels and, in some embodiments, is designed so as to not cause any substantial pressure drop in the flow of the primary coolant within the heat exchange sub-system that is used to vaporize a secondary coolant. In another embodiment, a nuclear reactor system is disclosed in which the reactor core is located below ground and all penetrations into the reactor pressure vessel are located above ground.