  Monte Carlo is a simple and flexible tool that is widely used in
computational finance. In this context, it is common for the quantity of
interest to be the expected value of a random variable defined via a stochastic
differential equation. In 2008, Giles proposed a remarkable improvement to the
approach of discretizing with a numerical method and applying standard Monte
Carlo. His multilevel Monte Carlo method offers an order of speed up given by
the inverse of epsilon, where epsilon is the required accuracy. So computations
can run 100 times more quickly when two digits of accuracy are required. The
multilevel philosophy has since been adopted by a range of researchers and a
wealth of practically significant results has arisen, most of which have yet to
make their way into the expository literature.
  In this work, we give a brief, accessible, introduction to multilevel Monte
Carlo and summarize recent results applicable to the task of option evaluation.
