  We review recent experimental and theoretical work on superconductivity in
ultrasmall metallic grains, i.e. grains sufficiently small that the conduction
electron energy spectrum becomes discrete. The discrete excitation spectrum of
an individual grain can be measured by the technique of single-electron
tunneling spectroscopy, and reveals parity effects indicative of pairing
correlations in the grain. After introducing the discrete BCS model that has
been used to model such grains, we review a phenomenological, grand-canonical,
variational BCS theory describing the paramagnetic breakdown of these pairing
correlations with increasing magnetic field. We also review recent canonical
theories that have been developed to describe how pairing correlations change
during the crossover, with decreasing grain size, from the bulk limit to the
limit of few electrons, and compare their results to those obtained using
Richardson's exact solution of the discrete BCS model. [The present review,
which is addressed at readers interested exclusively in superconducting aspects
of ultrasmall grains, is an excerpt from a more general review of ultrasmall
metallic grains, cond-mat/0101019, in which nonequilibrium excitations,
spin-orbit scattering, ferromagnetism and the effect of a magnetic impurity are
reviewed, too.]
