We investigate shock structure and particle acceleration in relativistic magnetized collisionless pair shocks by means of 2.5D and 3D particle-in-cell simulations . We explore a range of inclination angles between the pre-shock magnetic field and the shock normal . We find that only magnetic inclinations corresponding to “ subluminal ” shocks , where relativistic particles following the magnetic field can escape ahead of the shock , lead to particle acceleration . The downstream spectrum in such shocks consists of a relativistic Maxwellian and a high-energy power-law tail with exponential cutoff . For increasing magnetic inclination in the subluminal range , the high-energy tail accounts for an increasing fraction of particles ( from \sim 1 \% to \sim 2 \% ) and energy ( from \sim 4 \% to \sim 12 \% ) . The spectral index of the power law increases with angle from -2.8 \pm 0.1 to -2.3 \pm 0.1 . For nearly parallel shocks , particle energization mostly proceeds via the Diffusive Shock Acceleration process ; the upstream scattering is provided by oblique waves which are generated by the high-energy particles that escape upstream . For larger subluminal inclinations , Shock-Drift Acceleration is the main acceleration mechanism , and the upstream oblique waves regulate injection into the acceleration process . For “ superluminal ” shocks , self-generated shock turbulence is not strong enough to overcome the kinematic constraints , and the downstream particle spectrum does not show any significant suprathermal tail . As seen from the upstream frame , efficient acceleration in relativistic ( Lorentz factor \gamma _ { 0 } \gtrsim 5 ) magnetized ( \sigma \gtrsim 0.03 ) flows exists only for a very small range of magnetic inclination angles ( \lesssim 34 ^ { \circ } / \gamma _ { 0 } ) , so relativistic astrophysical pair shocks have to be either nearly parallel or weakly magnetized to generate nonthermal particles . These findings place constraints on the models of AGN jets , Pulsar Wind Nebulae and Gamma Ray Bursts that invoke particle acceleration in relativistic magnetized shocks .