  We give a brief overview of recent studies of weakly bound homonuclear
molecules in ultracold two-component Fermi gases. It is emphasized that they
represent novel composite bosons, which exhibit features of Fermi statistics at
short intermolecular distances. In particular, Pauli exclusion principle for
identical fermionic atoms provides a strong suppression of collisional
relaxation of such molecules into deep bound states. We then analyze
heteronuclear molecules which are expected to be formed in mixtures of
different fermionic atoms. It is found how an increase in the mass ratio for
the constituent atoms changes the physics of collisional stability of such
molecules compared to the case of homonuclear ones. We discuss Bose-Einstein
condensation of these composite bosons and draw prospects for future studies.
