Accreting neutron stars continue to surprise, from their short-timescale spin evolution, to the unexpected absence of spins faster than 700 Hz, their relativistic jets, and the pulsing ultra-luminous X-ray sources. I will present results of the first relativistic simulations of these systems, in both the force-free (high-magnetization) regime and using complete general-relativistic magnetohydrodynamics. Four distinct states are recovered, from crushing of the stellar magnetosphere to almost perfect exclusion of the accretion flow from the light cylinder by the pulsar's electromagnetic wind. A powerful Poynting-flux-dominated relativistic jet, driven by stellar rotation, is produced when the intruding plasma succeeds in "opening" the pulsar's previously closed (nearly dipolar) magnetic field lines. A simple analytic model can be useful in making estimates of stellar torques and jet powers. I will finish by discussing these results in the context of accreting pulsars' various observational manifestations.