  We first review the result that the noncommutative principal chiral model has
an infinite tower of conserved currents, and discuss the special case of the
noncommutative CP^1 model in some detail. Next, we focus our attention to a
submodel of the CP^1 model in the noncommutative spacetime A_\theta(R^2+1). By
extending a generalized zero curvature representation to A_\theta(R^2+1) we
discuss its integrability and construct its infinitely many conserved currents.
Supersymmetric principal chiral model with and without the WZW term and a
supersymmetric extension of the CP^1 submodel in noncommutative spacetime (i.e
in superspaces A_\theta(R^1+1|2), A_\theta(R^2+1|2)) are also examined in
detail and their infinitely many conserved currents are given in a systematic
manner. Finally, we discuss the solutions of the aforementioned submodels with
or without supersymmetry.
