  We describe the results that have so far been obtained in the classification
problem for integrable (2+1)-dimensional systems of hydrodynamic type. The
systems of Gibbons--Tsarev type are the most fundamental here. A whole class of
integrable (2+1)-dimensional models is related to each such system. We present
the known GT systems related to algebraic curves of genus g=0 and g=1 and also
a new GT system corresponding to algebraic curves of genus g=2. We construct a
wide class of integrable models generated by the simplest GT system, which was
not considered previously because it is in a sense trivial.
