The physics of charged particle acceleration is a key element of theoretical multi-messenger astrophysics. Particles that are accelerated to high energies may indeed escape from the source and thus add up to the cosmic ray spectrum, but they may also interact with ambient fields to produce high-energy neutrinos or photons. In this framework, electromagnetic turbulence plays a central role, because it governs the transport of particles inside the site of acceleration and because it offers itself a promising acceleration process, e.g.through particle-wave interactions.