  Percolation is the simplest fundamental model in statistical mechanics that
exhibits phase transitions signaled by the emergence of a giant connected
component. Despite its very simple rules, percolation theory has successfully
been applied to describe a large variety of natural, technological and social
systems. Percolation models serve as important universality classes in critical
phenomena characterized by a set of critical exponents which correspond to a
rich fractal and scaling structure of their geometric features. In this review
we will first outline the basic features of the ordinary model and take a
glimpse at a number of selective variations and modifications of the original
model. Directed percolation process will be also discussed as a prototype of
systems displaying a nonequilibrium phase transition. After a short review on
SLE, we will provide an overview on existence of the scaling limit and
conformal invariance of the critical percolation. We will also establish a
connection with the magnetic models. Recent applications of the percolation
theory in natural and artificial landscapes are also reviewed.
