  We consider imbalanced Fermi gases with strong attractive interactions, for
which Cooper-pair formation plays an important role. The two-component mixtures
consist either of identical fermionic atoms in two different hyperfine states,
or of two different atomic species both occupying only a single hyperfine
state. In both cases, the number of atoms for each component is allowed to be
different, which leads to a spin imbalance, or spin polarization. Two different
atomic species also lead to a mass imbalance. Imbalanced Fermi gases are
relevant to condensed-matter physics, nuclear physics and astroparticle
physics. They have been studied intensively in recent years, following their
experimental realization in ultracold atomic Fermi gases. The experimental
control in such a system allows for a systematic study of the equation of state
and the phase diagram as a function of temperature, spin polarization and
interaction strength. In this review, we discuss the progress in understanding
strongly-interacting imbalanced Fermi gases, where a main goal is to describe
the results of the highly controlled experiments. We start by discussing
Feshbach resonances, after which we treat the imbalanced Fermi gas in
mean-field theory to give an introduction to the relevant physics. We encounter
several unusual superfluid phases, including phase separation, gapless Sarma
superfluidity, and supersolidity. To obtain a more quantitative description of
the experiments, we review also more sophisticated techniques, such as
diagrammatic methods and the renormalization-group theory. We end the review by
discussing two theoretical approaches to treat the inhomogeneous imbalanced
Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes
approach.
