The supermassive black holes in the centres of active galaxies (AGN) eject powerful relativistic jets which propagate over kpc scales, showing no significant momentum loss. Both observational evidence as well as theoretical considerations from MHD simulations of jets suggest that they are radially stratified, with a fast inner spine surrounded by a slower-moving outer sheath. The resulting relativistic shear layers are a prime candidate for the site of relativistic particle acceleration in the jets of AGN and gamma-ray bursts (GRBs). We present results of particle-in-cell simulations of magnetic-field generation in the relativistic shear boundary layers of jets in AGN and GRBs. We outline future plans to include a self-consistent calculation of radiation produced by the particles accelerated at these shear boundary layers.