  The theory and numerical modelling of radiation processes and radiative
transfer play a key role in astrophysics: they provide the link between the
physical properties of an object and the radiation it emits. In the modern era
of increasingly high-quality observational data and sophisticated physical
theories, development and exploitation of a variety of approaches to the
modelling of radiative transfer is needed. In this article, we focus on one
remarkably versatile approach: Monte Carlo Radiative Transfer (MCRT). We
describe the principles behind this approach, and highlight the relative ease
with which they can (and have) been implemented for application to a range of
astrophysical problems. All MCRT methods have in common a need to consider the
adverse consequences of Monte Carlo noise in simulation results. We overview a
range of methods used to suppress this noise and comment on their relative
merits for a variety of applications. We conclude with a brief review of
specific applications for which MCRT methods are currently popular and comment
on the prospects for future developments.
