  Black widows and redbacks are binary millisecond pulsars with close low-mass
companions that are irradiated and gradually ablated by the pulsar's
high-energy luminosity $L_{\rm irr}$. These binaries evolve primarily through
magnetic braking, which extracts orbital angular momentum and pushes the
companion to overflow its Roche lobe. Here, we use the stellar evolution code
MESA to examine how the irradiation modifies the companion's structure. Strong
$L_{\rm irr}$ inhibits convection to the extent that otherwise fully convective
stars become almost fully radiative. By computing the convective velocities and
assuming a dynamo mechanism, we find that the thin convective envelopes of such
strongly irradiated companions ($L_{\rm irr}\gtrsim 3\,{\rm L}_\odot$) generate
much weaker magnetic fields than previously thought - halting binary evolution.
With our improved magnetic braking model, we explain most observed black widow
and redback companions as remnants of main-sequence stars. We also apply our
model (with $L_{\rm irr}$) to evolved companions that overflow their Roche lobe
close to the end of their main-sequence phase. The evolutionary tracks of such
companions bifurcate, explaining the shortest period systems (which are
potential gravitational wave sources) as well as the longest period ones (which
are the progenitors of common pulsar-white dwarf binaries). The variety of
black widow structures and evolutionary trajectories may be utilized to
calibrate the dependence of magnetic braking on the size of the convective
layer and on the existence of a radiative-convective boundary, with
implications for single stars as well as other binaries, such as cataclysmic
variables and AM Canum Venaticorum stars.
