  This survey article explores the notion of z-classes in groups. The concept
introduced here is related to the notion of orbit types in transformation
groups, and types or genus in the representation theory of finite groups of Lie
type. Two elements in a group are said to be z-equivalent (or z-conjugate) if
their centralizers are conjugate. This is a weaker notion than the conjugacy of
elements. In this survey article, we present several known results on this
topic and suggest some further questions.
