A detailed model is constructed for the spacetime of an evaporating black hole. This model is used to analyze some persistent questions about black hole spacetimes in general, and to discuss the mechanism of Hawking radiation. The self-consistency of the model is studied and used to illuminate some general principles in semiclassical gravity. Along the way, a unified analysis is provided for the class of ``strongly spherically symmetric'' spacetimes, and a method for constructing a broad class of explicit Penrose diagrams is obtained
