  Lyapunov's second or direct method is one of the most widely used techniques
for investigating stability properties of dynamical systems. This technique
makes use of an auxiliary function, called a Lyapunov function, to ascertain
stability properties for a specific system without the need to generate system
solutions. An important question is the converse or reversability of Lyapunov's
second method; i.e., given a specific stability property does there exist an
appropriate Lyapunov function? We survey some of the available answers to this
question.
