  Mathematical models are an important tool for neuroscientists. During the
last thirty years many papers have appeared on single neuron description and
specifically on stochastic Integrate and Fire models. Analytical results have
been proved and numerical and simulation methods have been developed for their
study. Reviews appeared recently collect the main features of these models but
do not focus on the methodologies employed to obtain them. Aim of this paper is
to fill this gap by upgrading old reviews on this topic. The idea is to collect
the existing methods and the available analytical results for the most common
one dimensional stochastic Integrate and Fire models to make them available for
studies on networks. An effort to unify the mathematical notations is also
made. This review is divided in two parts: Derivation of the models with the
list of the available closed forms expressions for their characterization;
Presentation of the existing mathematical and statistical methods for the study
of these models.
