  These notes survey the first results on large deviations of Schramm-Loewner
evolutions (SLE) with emphasis on interrelations between 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.
