The aim of this book is to provide the reader with a guide to Hawking radiation through a dual approach to the problem. In the first part of Hawking Radiation, the authors summarise some basic knowledge about black holes and quantum field theory in curved spacetime. In the second part, they present a survey of methods for deriving and studying Hawking radiation from astrophysical black holes, from the original calculation by S.W. Hawking to the most recent contributions involving gravitational anomalies and tunnelling. In the third part, they introduce analogue gravity models, with particular attention to dielectric black hole systems, to which the studies of the present authors are devoted. The mutual interchange of knowledge between the aforementioned parts is addressed to render a more comprehensive picture of this very fascinating quantum phenomenon associated with black holes.