  The creation of stable 1D and 2D localized modes in lossy nonlinear media is
a fundamental problem in optics and plasmonics. This article gives a short
review of theoretical methods elaborated for this purpose, using localized gain
applied at one or several "hot spots" (HSs). The introduction surveys a broad
class of models for which this approach was developed. Other sections focus in
some detail on basic 1D continuous and discrete systems, where the results can
be obtained, partly or fully, in an analytical form (verified by comparison
with numerical results), which provides a deeper insight into the nonlinear
dynamics of optical beams in dissipative nonlinear media. In particular,
considered are the single and double HSs in the usual waveguide with the
self-focusing (SF) or self-defocusing (SDF) Kerr nonlinearity, which give rise
to rather sophisticated results, in spite of apparent simplicity of the model;
solitons attached to a PT-symmetric dipole embedded into the SF or SDF medium;
gap solitons pinned to an HS in a Bragg grating; and discrete solitons in a 1D
lattice with a "hot site".
