  There are now about fifty known radio pulsars in binary systems, including at
least five in double neutron star binaries. In some cases, the stellar masses
can be directly determined from measurements of relativistic orbital effects.
In others, only an indirect or statistical estimate of the masses is possible.
We review the general problem of mass measurement in radio pulsar binaries, and
critically discuss all current estimates of the masses of radio pulsars and
their companions. We find that significant constraints exist on the masses of
twenty-one radio pulsars, and on five neutron star companions of radio pulsars.
All the measurements are consistent with a remarkably narrow underlying
gaussian mass distribution, m = 1.35 +- 0.04 solar masses. There is no evidence
that extensive mass accretion (delta m >~ 0.1 solar mass) has occurred in these
systems. We also show that the observed inclinations of millisecond pulsar
binaries are consistent with a random distribution, and thus find no evidence
for either alignment or counteralignment of millisecond pulsar magnetic fields.
