In this review I discuss the characteristics and the formation of all classes
of millisecond pulsars (MSPs). The main focus is on the stellar astrophysics of
X-ray binaries leading to the production of fully recycled MSPs with white
dwarf (WD) or substellar semi-degenerate companions. Depending on the nature of
the companion star MSPs are believed to form from either low-mass X-ray
binaries (LMXBs) or intermediate-mass X-ray binaries (IMXBs). For each of these
two classes of X-ray binaries the evolutionary status of the donor star -- or
equivalently, the orbital period -- at the onset of the Roche-lobe overflow
(RLO) is the determining factor for the outcome of the mass-transfer phase and
thus the nature of the MSP formed. Furthermore, the formation of binary MSPs is
discussed in context of the (P,P_dot)-diagram, as well as new interpretations
of the Corbet diagram. Finally, I present new models of Case A RLO of IMXBs in
order to reproduce the two solar mass pulsar PSR J1614-2230.Comment: 17 pages, 9 figures (color). Invited review at ESO workshop
"Evolution of Compact Binaries", March 2011, Vina del Mar (Chile), ASP Conf.
Series. Fig.7 is available in high resolution on reques