I will discuss how the dynamical evaporation of a black hole through quantum Hawking emission admits a dual description in terms of classical gravitational evolution in Anti-de Sitter space. The idea was first proposed two decades ago, but it remained underdeveloped and poorly understood due to conceptual subtleties and technical difficulties. Recently, in collaboration with Luna, Suzuki, Tomasevic and Way, we have applied novel methods to study the dual dynamical evaporation of a variety of black holes interacting with colder radiation systems. We have also obtained the dual of the collapse of holographic radiation to form a black hole on the brane.