  In this paper, we give a summary of stability criteria that have been derived
for hierarchical triple systems over the past few decades. We give a brief
description and we discuss the criteria that are based on the generalisation of
the concept of zero velocity surfaces of the restricted three body problem, to
the general case. We also present criteria that have to do with escape of one
of the bodies. Then, we talk about the criteria that have been derived using
data from numerical integrations. Finally, we report on criteria that involve
the concept of chaos. In all cases, wherever possible, we discuss advantages
and disadvantages of the criteria and the methods their derivation was based
on, and some comparison is made in several cases.
