  This paper is an overview of the classical level crossing problem which is
studied extensively in the literature and is fundamental in many branches of
applied probability. We discuss a number of approximations with an emphasis on
their performance, methods of justification and technical conditions which are
required in these methods, including a new approximation called "inverse
Gaussian". It is derived by a new method, is fruitful for solving related
problems, and is valid under mild regularity conditions. We emphasize its
novelty and boons.
