This is an introductory account of the emergence of conformal invariance in
the scaling limit of planar critical percolation. We give an exposition of
Smirnov's theorem (2001) on the conformal invariance of crossing probabilities
in site percolation on the triangular lattice. We also give an introductory
account of Schramm-Loewner evolutions (SLE(k)), a one-parameter family of
conformally invariant random curves discovered by Schramm (2000). The article
is organized around the aim of proving the result, due to Smirnov (2001) and to
Camia and Newman (2007), that the percolation exploration path converges in the
scaling limit to chordal SLE(6). No prior knowledge is assumed beyond some
general complex analysis and probability theory.Comment: 55 pages, 10 figure