  We outline a new approach to the characterization as well as to the
classification of positive maps. This approach is based on the facial
structures of the set of states and of the cone of positive maps. In
particular, the equivalence between Schroedinger's and Heisenberg's pictures is
reviewed in this more general setting. Furthermore, we discuss in detail the
structure of positive maps for two and three dimensional systems. In
particular, the explicit form of decomposition of a positive map and the
uniqueness of this decomposition for extremal positive maps for 2 dimensional
case are described. The difference of the structure of positive maps between 2
dimensional and 3 dimensional cases is clarified. The resulting
characterization of positive maps is applied to the study of quantum
correlations and entanglement
