  We present the results of a systematic study of the formation and evolution
of binaries containing black holes and normal-star companions with a wide range
of masses. We first reexamine the standard formation scenario for close
black-hole binaries, where the spiral-in of the companion in the envelope of a
massive star causes the ejection of the envelope. We estimate the formation
rates for different companion masses and different assumptions about the
common-envelope structure and other model parameters. We find that black-hole
binaries with intermediate- and high-mass secondaries can form for a wide range
of assumptions, while black-hole binaries with low-mass secondaries can only
form with apparently unrealistic assumptions (in agreement with previous
studies). We then present detailed binary evolution sequences for black-hole
binaries with secondaries of 2 to 17 Msun and demonstrate that in these systems
the black hole can accrete appreciably even if accretion is Eddington limited
(up to 7 Msun for an initial black-hole mass of 10 Msun) and that the black
holes can be spun up significantly in the process. We discuss the implications
of these calculations for well-studied black-hole binaries (in particular GRS
1915+105), ultra-luminous X-ray sources and Cygnus X-1. Finally, we discuss how
some of the assumptions in the standard model could be relaxed to allow the
formation of low-mass, short-period black-hole binaries which appear to be very
abundant in Nature. (Abstract abridged)
