Hawking radiation, despite being known to theoretical physics for nearly forty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from practical and conceptual difficulties. Of particular note is the trans-Planckian problem, which is concerned with the apparent origin of the radiation in absurdly high frequencies. In order to gain better theoretical understanding and, it is hoped, experimental verification of Hawking radiation, much

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... y is being devoted to laboratory systems which use moving media to model the spacetime geometry of black holes, and which, by analogy, are also thought to emit Hawking radiation. These analogue systems typically exhibit dispersion, which regularizes the wave behaviour at the horizon at the cost of a more complicated theoretical framework. This tutorial serves as an introduction to Hawking radiation and its analogues, developing the moving medium analogy for black holes and demonstrating how dispersion can be incorporated into this generalized framework.