  Kramers' law describes the mean transition time of an overdamped Brownian
particle between local minima in a potential landscape. We review different
approaches that have been followed to obtain a mathematically rigorous proof of
this formula. We also discuss some generalisations, and a case in which
Kramers' law is not valid. This review is written for both mathematicians and
theoretical physicists, and endeavours to link concepts and terminology from
both fields.
