  A brief review is given of some well-known and some very recent results
obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both
zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are
considered. Physical realizations of multidimensional solitons in atomic
Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed
too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are
vulnerable to instabilities induced by the occurrence of the critical and
supercritical collapse, respectively, in the same 2D and 3D models that give
rise to the solitons. Vortex solitons are subject to a still stronger splitting
instability. For this reason, a central problem is search for physical settings
in which 2D and 3D solitons may be stabilized. The brief review addresses one
well-established topic, viz., the stabilization of the 3D and 2D states, with S
= 0 and 1, trapped in harmonic-oscillator (HO) potentials, and another topic
which was developed very recently: the stabilization of 2D and 3D free-space
solitons, which juxtapose components with S = 0 and (+/-)1 (semi-vortices and
mixed modes), in a binary system with the spin-orbit coupling (SOC) between its
components. The former model is based on the single cubic nonlinear
Schroedinger/Gross-Pitaevskii equation (NLSE/GPE), while the latter one is
represented by a system of two coupled GPEs. In both cases, generic situations
are drastically different in the 2D and 3D geometries. In the 2D settings, the
stabilization mechanism creates a stable ground state (GS, which was absent
without the stabilization), whose norm falls below the threshold value at which
the critical collapse sets in. In the 3D geometry, the supercritical collapse
does not allow to create a GS, but metastable solitons can be constructed.
