We present an overview of the various phase transitions that we anticipate to
occur in trapped fermionic alkali gases. We also discuss the prospects of
observing these transitions in (doubly) spin-polarized Li-6 and K-40 gases,
which are now actively being studied by various experimental groups around the
world.Comment: 18 pages of LaTeX and 2 postscript figures. Contribution to the
international summer school `Enrico Fermi' on Bose-Einstein condensation in
atomic gases, Varenna 199