  We review topics related to the first moment of azimuthal anisotropy ($v_1$),
commonly known as directed flow, focusing on both charged particles and
identified particles from heavy-ion collisions. Beam energies from the highest
available, at the CERN LHC, down to projectile kinetic energies per nucleon of
a few GeV per nucleon, as studied in experiments at the Brookhaven AGS, fall
within our scope. We focus on experimental measurements and on theoretical work
where direct comparisons with experiment have been emphasized. The physics
addressed or potentially addressed by this review topic includes the study of
Quark Gluon Plasma, and more generally, investigation of the Quantum
Chromodynamics phase diagram and the equation of state describing the
accessible phases.
