  We review recent results on new physical models constructed as PT-symmetrical
deformations or extensions of different types of integrable models. We present
non-Hermitian versions of quantum spin chains, multi-particle systems of
Calogero-Moser-Sutherland type and non-linear integrable field equations of
Korteweg-de-Vries type. The quantum spin chain discussed is related to the
first example in the series of the non-unitary models of minimal conformal
field theories. For the Calogero-Moser-Sutherland models we provide three
alternative deformations: A complex extension for models related to all types
of Coxeter/Weyl groups; models describing the evolution of poles in constrained
real valued field equations of non linear integrable systems and genuine
deformations based on antilinearly invariant deformed root systems.
Deformations of complex nonlinear integrable field equations of KdV-type are
studied with regard to different kinds of PT-symmetrical scenarios. A reduction
to simple complex quantum mechanical models currently under discussion is
presented.
