Simplified nuclear reactors include depressurization systems or gravity-driven injection systems or both. The systems depressurize and cool the reactor without operator intervention and power. An underground containment building may be used with the depressurization and injection systems passing through the same from above ground. Depressurization systems may use a rupture disk, relief line, pool, and filter to open the reactor and carry coolant away for condensation and exhausting. Injection systems may use a coolant tank above the nuclear reactor to inject liquid coolant by gravity into the reactor through an injection line and valve. The rupture disk and valve may be integral with the reactor and use penetration seals where systems pass through containment. Rupture disks and valves can actuate passively, at a pressure setpoint or other condition, through fluidic controls, setpoint failure, etc. The depressurization system and injection system together feed-and-bleed coolant through the reactor.