Abstract. The number of pulsars with detected emission at X-ray and γ-ray energies has been steadily growing, showing that beams of high-energy particles are commonly accelerated in pulsar magnetospheres, even though the location and number of acceleration sites remain unsettled. Acceleration near the magnetic poles, close to the polar cap surface or to higher altitudes in the slot gap along the last open field lines, involves an electric field component due to inertial-frame dragging. Acceleration can also take place in the outer magnetosphere where charge depletion due to global currents causes a large electric field along the magnetic field lines. All models require a detailed knowledge of the open magnetosphere geometry and its relativistic distortions. Observational trends with age, spin-down power and magnetic field as well as population synthesis studies in the Galactic disc and the nearby Gould Belt provide useful, however not yet conclusive, constraints on the competing models.