I review the evolutionary connection between low-mass X-ray binaries (LMXBs)
and pulsars with binary companions (bPSRs) from a stellar binary evolution
perspective. I focus on the evolution of stellar binaries with end-states
consisting of a pulsar with a low-mass (<1.0 solar mass) companion, starting at
the point the companion's progenitor first initiates mass transfer onto the
neutron star. Whether this mass transfer is stable and the physics driving
ongoing mass transfer partitions the phase space of the companions's initial
mass and initial orbital period into five regions. The qualitative nature of
the mass-transfer process and the binary's final end-state differ between
systems in each region; four of these regions each produce a particular class
of LMXBs. I compare the theoretical expectations to the populations of galactic
field LMXBs with companion-mass constraints and field bPSRs. I show that the
population of accreting millisecond pulsars are all identified with only two of
the four LMXB classes and that these systems do not have readily identifiable
progeny in the bPSR population. I discuss which sub-populations of bPSRs can be
explained by binary evolution theory and those that currently are not. Finally
I discuss some outstanding questions in this field.Comment: 9 pages, 5 figures, to appear in the proceedings of the 40 Years of
Pulsars conference held at McGill University in August 200