  These notes survey the first and recent results on large deviations of
Schramm-Loewner evolutions (SLE) with the emphasis on interrelations among rate
functions and applications to complex analysis. More precisely, we describe the
large deviations of SLE$_\kappa$ when the $\kappa$ parameter goes to zero in
the chordal and multichordal case and to infinity in the radial case. The rate
functions, namely Loewner and Loewner-Kufarev energies, are closely related to
the Weil-Petersson class of quasicircles and real rational functions.
