  The aim of this work is to review the tunnelling method as an alternative
description of the quantum radiation from black holes and cosmological
horizons. The method is first formulated and discussed for the case of
stationary black holes, then a foundation is provided in terms of analytic
continuation throughout complex space-time. The two principal implementations
of the tunnelling approach, which are the null geodesic method and the
Hamilton-Jacobi method, are shown to be equivalent in the stationary case. The
Hamilton-Jacobi method is then extended to cover spherically symmetric
dynamical black holes, cosmological horizons and naked singularities. Prospects
and achievements are discussed in the conclusions.
