  We review the status of cooling techniques aimed at achieving the deepest
quantum degeneracy for atomic Fermi gases. We first discuss some physical
motivations, providing a quantitative assessment of the need for deep quantum
degeneracy in relevant physics cases, such as the search for unconventional
superfluid states. Attention is then focused on the most widespread technique
to reach deep quantum degeneracy for Fermi systems, sympathetic cooling of
Bose-Fermi mixtures, organizing the discussion according to the specific
species involved. Various proposals to circumvent some of the limitations on
achieving the deepest Fermi degeneracy, and their experimental realizations,
are then reviewed. Finally, we discuss the extension of these techniques to
optical lattices and the implementation of precision thermometry crucial to the
understanding of the phase diagram of classical and quantum phase transitions
in Fermi gases.
