  This survey covers the mathematical theory of steady water waves with an
emphasis on topics that are at the forefront of current research. These areas
include: variational characterizations of traveling water waves; analytical and
numerical studies of periodic waves with critical layers that may overhang;
existence, nonexistence, and qualitative theory of solitary waves and fronts;
traveling waves with localized vorticity or density stratification; and waves
in three dimensions.
