The paper contains a review of results concerning the theory of iterated fu
nction systems (IFS) acting on an arbitrary metric space (without any assum
ption of compactness). First we discuss IFS acting on sets and we define fr
actals and semifractals using topological limits. Then me study IFS with pr
obabilities acting on measures and we show a relationship with the theory o
f Markov operators and Markov processes.