We present a real-time neural radiance caching method for path-traced global illumination. Our system is designed to handle fully dynamic scenes, and makes no assumptions about the lighting, geometry, and materials. The data-driven nature of our approach sidesteps many difficulties of caching algorithms, such as locating, interpolating, and updating cache points. Since pretraining neural networks to handle novel, dynamic scenes is a formidable generalization challenge, we do away with pretraining and instead achieve generalization via adaptation, i.e. we opt for training the radiance cache while rendering. We employ self-training to provide low-noise training targets and simulate infinite-bounce transport by merely iterating few-bounce training updates. The updates and cache queries incur a mild overhead -- about 2.6ms on full HD resolution -- thanks to a streaming implementation of the neural network that fully exploits modern hardware. We demonstrate significant noise reduction at the cost of little induced bias, and report state-of-the-art, real-time performance on a number of challenging scenarios.