Self-similar models are important in general relativity and other fundamental
theories. In this paper we shall discuss the ``similarity hypothesis'', which
asserts that under a variety of physical circumstances solutions of these
theories will naturally evolve to a self-similar form. We will find there is
good evidence for this in the context of both spatially homogenous and
inhomogeneous cosmological models, although in some cases the self-similar
model is only an intermediate attractor. There are also a wide variety of
situations, including critical pheneomena, in which spherically symmetric
models tend towards self-similarity. However, this does not happen in all cases
and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra
