We review the various ways in which binary pulsars, millisecond pulsars and pulsars in globular clusters may have formed. To this end the formation processes of neutron stars in interacting binaries, and the subsequent evolution of such systems are discussed.In section 2 the observed properties of radio pulsars, single as well as in binaries, are briefly reviewed. The peculiar combination of rapid spin and relatively weak magnetic fields of the binary and millisecond pulsars and the high incidence of binaries among millisecond pulsars strongly suggest that many of them (if not all) are old neutron stars that have been ``recycled'' by the accretion of mass and angular momentum from a companion star in a mass-transfer binary. Recycled pulsars are expected to represent a later evolutionary phase of various observed types of binary X-ray sources. In section 3 the observed properties of the various types of binary X-ray sources are summarized, and the evolutionary history of close binary systems leading to the formation of X-ray binaries is reviewed. In view of the relevance for the later evolution of X-ray binaries into binary and millisecond pulsars, we discuss in this section also the effect of various types of accretion (from a stellar wind, and by Roche-lobe overflow) on the spin evolution of accreting magnetized neutron stars. Subsequently the later evolution and final evolutionary products of X-ray binaries are discussed. Massive X-ray binaries may in the end either leave (i) a very close binary pulsar consisting of two neutron stars (with an eccentric orbit) or a neutron star and a massive white dwarf with a circular orbit, or (ii) two runaway pulsars, one newborn and one recycled, or (iii) a single low-velocity recycled pulsar. Low-mass X-ray binaries may either leave relatively wide binaries with circular orbits consisting of a low-mass (0.2-0.4Msolar) white dwarf and a recycled neutron star, or a single recycled neutron star which has ``evaporated'' its companion star, or possibly has merged with it. We also discuss in this section the possible origin of the velocity-magnetic field correlation observed in single radio pulsars. The correlation can be obtained by a combination of close binary evolution and the occurrence of asymmetries in supernova mass ejection or, alternatively, by a combination of close binary evolution and the evaporation of low-mass companions to young pulsars. Section 4 is devoted to the special formation and evolution processes of close neutron star binaries that operate in globular star clusters. The high incidence of pulsars (mostly binary and/or millisecond pulsars) in globular clusters and the origin of the relatively large fraction (>~ 50%) of single pulsars among them is discussed. From the discussions in section 4 and section 5 it is concluded that so far no clear evidence - nor the need - for the formation of neutron stars (millisecond pulsars) by the accretion-induced collapse of white dwarfs in globular clusters has been presented, although this formation mechanism cannot be excluded. For the formation of low-mass X-ray binaries in the galactic disk this mechanism, however, may make a significant contribution. In section 5 the statistical properties of the binary and millisecond pulsars in globular clusters and in the general field are discussed in relation to the evolution of neutron star magnetic fields. The following conclusions are drawn: (i) There is no longer clear evidence that the magnetic fields of isolated neutron stars (radio pulsars) do decay. (ii) Neutron stars that have been recycled by accretion in close binaries do show clear evidence for magnetic field decay. This field decay may be due to either (a) the accretion process itself or (b) the spin evolution of the neutron stars in binaries which has affected the magnetic field carried by the liquid interior of the neutron star. (iii) A sizeable fraction of all observed single radio pulsars (of order several tens of per cent) may have been recycled in (mostly massive) close binaries. The presence of this group in the general pulsar population may have created the impression that the magnetic fields of single neutron stars do decay. In section 6 the findings of earlier sections are summarized and some open problems are listed. On leave from Raman Research Institute, Bangalore, India.