Hawking radiation : from astrophysical black holes to analogous systems in lab The aim of this book is to provide the reader with a guide to Hawking radiation through a dual approach to the problem. After a introductory chapter containing some basic knowledge about black holes and quantum field theory in curved spacetime the first part of the book consists in 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 tunneling and gravitational anomalies. In the second part we introduce analogue gravity and we focus our 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 A short scrapbook on classical black holes The seminal paper Thermality of Hawking radiation: from Hartle Hawking to Israel and Unruh The tunneling approach The anomaly route to Hawking radiation The Euclidean section and Hawking temperature Rigorous aspects of Hawking radiation The roots of analogue gravity Hawking radiation in a non dispersive nonlinear Kerr dielectric Hawking radiation in a dispersive Kerr dielectric Hawking radiation in the lab