  In recent years, important progress has been made in the field of
two-dimensional statistical physics. One of the most striking achievements is
the proof of the Cardy-Smirnov formula. This theorem, together with the
introduction of Schramm-Loewner Evolution and techniques developed over the
years in percolation, allow precise descriptions of the critical and
near-critical regimes of the model. This survey aims to describe the different
steps leading to the proof that the infinite-cluster density $\theta(p)$ for
site percolation on the triangular lattice behaves like $(p-p_c)^{5/36+o(1)}$
as $p\searrow p_c=1/2$.
