  We propose a systematic treatment of symmetries of KP integrable systems,
including constrained (reduced) KP models ${\sl cKP}_{R,M}$, and their
multi-component (matrix) generalizations. Any such integrable hierarchy is
shown to possess an additional $({\hat U}(1)\oplus{\hat {SL}}(M))_{+} \oplus
({\hat {SL}}(M+R))_{-}$ loop-algebra symmetry. Also we provide a systematic
construction of the full algebra of Virasoro additional symmetries in the case
of constrained KP models which requires a nontrivial modification of the known
Orlov-Schulman construction for the general unconstrained KP hierarchy.
Multi-component KP hierarchies are identified as ordinary (scalar)
one-component KP hierarchies supplemented with the Cartan subalgebra of the
additional symmetry algebra, which provides the basis of a new method for
construction of soliton-like solutions. Davey-Stewartson and $N$-wave resonant
systems arise as symmetry flows of ordinary ${\sl cKP}_{R,M}$ hierarchies.
