  In this chapter the recent theoretical work on phase transition in imbalanced
fermion superfluids is reviewed. The imbalanced systems are those in which the
two fermionic species candidate to form pairing have different Fermi surfaces
or densities. We consider systems subjected to weak interactions. In this
scenario two distinct phase transitions are predicted to occur. A
thermodynamical phase transition, induced by the temperature (T), and a quantum
phase transition as a function of the increasing chemical potentials asymmetry,
that takes place at zero temperature. We also briefly discuss some recent
experimental work at non-zero T with imbalanced Fermi gases in cold atomic
traps.
