  An orbital ordering occurs in many transition metal compounds with
Jahn-Teller ions and plays an important role in these materials. At the same
time, exchange interactions in orbitally degenerate systems are inherently
frustrated, even in materials with simple crystal lattices. We discuss the
origin of this frustration, considering in detail materials with a cubic and
triangular lattice of transition metal ions. We also discuss possible types of
ground states of such systems, e.g., disordered orbital liquids and ordering
due to the order-from-disorder mechanism.
