Five and a Half Roads to Form a Millisecond Pulsar

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 PP-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.

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