Both observational evidence and theoretical considerations suggest that the relativistic jets of AGN and gamma-ray bursts are likely to be radially stratified with a fast, inner spine and a slower outer sheath. The resulting relativistic shear layer is expected to be a site of self-generation of magnetic fields due to the Weibel instability, and of relativistic particle acceleration. We here present first results of particle-in-cell (PIC) simulations of relativistic shear layers in both electron-proton and electron-positron jets. We demonstrate that magnetic fields close to equipartition can be self-generated in initially unmagnetized flows, and MHD turbulence in the shear layer leads to the acceleration of highly anisotropic particle distributions. We will discuss the expected radiative (synchrotron + Compton) signatures, considering both their spectral shape and polarization.