The experimental realization of ultracold Fermi gases near a Feshbach resonance
allows to study gases with attractive interactions of essentially arbitrary strength. They
extend the classic paradigm of superconductivity caused by the formation and
simultaneous condensation of Cooper pairs into a regime, which has never been accessible before.
I will give an introduction to the subject and in particular to the prospects of
realizing pairs with finite center-of-mass momentum predicted long ago by Fulde and Ferrell
and by Larkin and Ovchinnikov.