  Superfluidity or superconductivity with mismatched Fermi momenta appears in
many systems such as charge neutral dense quark matter, asymmetric nuclear
matter, and in imbalanced cold atomic gases. The mismatch plays the role of
breaking the Cooper pairing, and the pair-breaking state cannot be properly
described in the framework of standard BCS theory. I give a brief review on
recent theoretical development in understanding unconventional color
superconductivity, including gapless color superconductor, the chromomagnetic
instabilities and the Higgs instability in the gapless phase. I also introduce
a possible new framework for describing unconventional color superconductor.

High Energy Physics - Phenomenology