  The use of Feshbach resonances for tuning the interparticle interaction in
ultracold Fermi gases has led to remarkable developments, in particular to the
creation and Bose-Einstein condensation of weakly bound diatomic molecules of
fermionic atoms. These are the largest diatomic molecules obtained so far, with
a size of the order of thousands of angstroms. They represent novel composite
bosons, which exhibit features of Fermi statistics at short intermolecular
distances. Being highly excited, these molecules are remarkably stable with
respect to collisional relaxation, which is a consequence of the Pauli
exclusion principle for identical fermionic atoms. The purpose of this review
is to introduce theoretical approaches and describe the physics of molecular
regimes in two-component Fermi gases and Fermi-Fermi mixtures, focusing
attention on quantum statistical effects.
