  Self-projective sets are natural fractal sets which describe the action of a
semigroup of matrices on projective space. In recent years there has been
growing interest in studying the dimension theory of self-projective sets, as
well as progress in the understanding of closely related objects such as
Furstenberg measures. The aim of this survey is twofold: first to motivate the
study of these objects from several different perspectives and second to make
the study of these objects more accessible for readers with expertise in
iterated function systems.
