  Recent experiments on conduction between a semiconductor and a superconductor
have revealed a variety of new mesoscopic phenomena. Here is a review of the
present status of this rapidly developing field. A scattering theory is
described which leads to a conductance formula analogous to Landauer's formula
in normal-state conduction. The theory is used to identify features in the
conductance which can serve as "signatures" of phase-coherent Andreev
reflection, i.e. for which the phase coherence of the electrons and the
Andreev-reflected holes is essential. The applications of the theory include a
quantum point contact, quantum dot, weak localization, universal conductance
fluctuations, shot noise, and reflectionless tunneling. This review is based on
lectures at the Les Houches summer school, Session LXI, 1994.
