  We review recent results concerning the mathematical properties of the
Bardeen-Cooper-Schrieffer (BCS) functional of superconductivity, which were
obtained in a series of papers partly in collaboration with R. Frank, E. Hamza,
S. Naboko, and J.P. Solovej. Our discussion includes, in particular, an
investigation of the critical temperature for a general class of interaction
potentials, as well as a study of its dependence on external fields. We shall
explain how the Ginzburg-Landau model can be derived from the BCS theory in a
suitable parameter regime.
