  This is a survey on reproducing kernel Krein spaces and their interplay with
operator valued Hermitian kernels. Existence and uniqueness properties are
carefully reviewed. The approach we follow in this survey uses a more abstract
but very useful concept of linearization or Kolmogorov decomposition, as well
as the underlying concept of Krein space induced by a selfadjoint operator and
that of Krein space continuously embedded. The operator range feature of
reproducing kernel spaces is emphasized. We include a careful presentation of
Hermitian kernels on complex regions that points out a universality property of
the Szego kernels with respect to reproducing kernel Krein spaces of
holomorphic functions.
