  We explore the relationship between limit spaces of contracting self-similar
groups and self-similar structures. We give the condition on a contracting
group such that its limit space admits a self-similar structure, and also the
condition such that this self-similar structure is p.c.f. We then give the
necessary and sufficient condition on a p.c.f. self-similar structure such that
there exists a contracting group whose limit space has an isomorphic
self-similar structure; in this case, we provide a construction that produces
such a contracting group. Finally, we illustrate our results with several
examples.
