Explicitly computed Penrose diagrams are plotted for a classical model of black hole formation and evaporation, in which black holes form by the accretion of infalling spherical shells of matter and subsequently evaporate by emitting spherical shells of Hawking radiation. This model is based on known semiclassical effects, but is not a full solution of semiclassical gravity. The method allows arbitrary interior metrics of the form $ds^2=-f(r),dt^2+f(r)^{-1},dr^2+r^2,dOmega^2$, including singular and nonsingular models. Matter dynamics are visualized by explicitly plotting proper density in the diagrams, as well as by tracking the location of trapped surfaces and energy condition violations. The most illustrative model accurately approximates the standard time evolution for black hole thermal evaporation; its time dependence and causal structure are analyzed by inspection of the diagram. The resulting insights contradict some common intuitions and assumptions, and we point out some examples in the literature with assumptions that do not hold up in this more detailed model. Based on the new diagrams, we argue for an improved understanding of the Hawking radiation process, propose an alternate definition of black hole in the presence of evaporation, and suggest some implications regarding information preservation and unitarity.
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