  We examine how tides, stellar evolution, and magnetic braking shape the
rotation period (P$_{rot}$) evolution of low-mass stellar binaries up to
orbital periods (P$_{orb}$) of 100 d across a wide range tidal dissipation
parameters using two common equilibrium tidal models. We find that many
binaries with P$_{orb} < 20$ d tidally lock, and most with $P_{orb} < 4$ d
tidally lock into synchronous rotation on circularized orbits. At short
P$_{orb}$, tidal torques produce a population of fast rotators that single-star
only models of magnetic braking fail to produce. In many cases, we show that
the competition between magnetic braking and tides produces a population of
subsynchronous rotators that persists for Gyrs, even in short P$_{orb}$
binaries, qualitatively reproducing the subsynchronous eclipsing binaries (EBs)
discovered in the Kepler field by Lurie et al. (2017). Both equilibrium tidal
models predict that binaries can tidally-interact out to P$_{orb} \approx 80$
d, while the Constant Phase Lag tidal model predicts that binaries can tidally
lock out to P$_{orb} \approx 100$ d. Tidal torques often force the P$_{rot}$
evolution of stellar binaries to depart from the long-term magnetic
braking-driven spin down experienced by single stars, revealing that P$_{rot}$
is not be a valid proxy for age in all cases, i.e. gyrochronology can
underpredict ages by up to $300\%$ unless one accounts for binarity. We suggest
that accurate determinations of orbital eccentricties and P$_{rot}$ can be used
to discriminate between which equilibrium tidal models best describes tidal
interactions in low-mass binary stars.
