  The properties of transition metal compounds are largely determined by
nontrivial interplay of different degrees of freedom: charge, spin, lattice,
but also orbital ones. Especially rich and interesting effects occur in systems
with orbital degeneracy. They result in the famous Jahn-Teller effect leading
to a plethora of consequences, in static and in dynamic properties, including
nontrivial quantum effects. In the present review we discuss the main phenomena
in the physics of such systems, paying central attention to the novel
manifestations of those. After shortly summarising the basic phenomena and
their description, we concentrate on several specific directions in this field.
One of them is the reduction of effective dimensionality in many systems with
orbital degrees of freedom due to directional character of orbitals, with
concomitant appearance of some instabilities leading in particular to the
formation of dimers, trimers and similar clusters in a material. The properties
of such cluster systems, largely determined by their orbital structure, are
discussed in detail, and many specific examples of those in different materials
are presented. Another big field which acquired special significance relatively
recently is the role of relativistic spin-orbit interaction. The mutual
influence of this interaction and the more traditional Jahn-Teller physics is
treated in details in the second part of the review. In discussing all these
questions special attention is paid to novel quantum effects in those.
