  Optical vortices are phase singularities nested in electromagnetic waves that
constitute a fascinating source of phenomena in the physics of light and
display deep similarities to their close relatives, quantized vortices in
superfluids and Bose-Einstein condensates. We present a brief overview of the
major advances in the study of optical vortices in different types of nonlinear
media, with emphasis on the properties of {\em vortex solitons}. Self-focusing
nonlinearity leads, in general, to the azimuthal instability of a
vortex-carrying beam, but it can also support novel types of stable or
meta-stable self-trapped beams carrying nonzero angular momentum, such as
ring-like solitons, necklace beams, and soliton clusters. We describe vortex
solitons created by multi-component beams, by parametrically coupled beams in
quadratic nonlinear media, and in partially incoherent light, as well as
discrete vortex solitons in periodic photonic lattices.
