The nature of the radiative processes responsible for prompt and afterglow emission in Gamma-Ray Bursts (GRB) is far from being understood. The lack of a clear understanding on how radiation is produced is strictly related to other fundamental open questions in GRB physics, such as the jet composition (magnetic or baryonic), the location of the emitting region, and the nature of mechanisms regulating energy dissipation and particle acceleration. In this talk, I present some recent developments in the field. In the context of afterglow emission, I discuss the origin of high-energy (GeV) radiation detected in around 100 GRBs by the Fermi-LAT and the prospects for GRB detection with the CTA. In the context of prompt radiation, I present new, unexpected features recently discovered in prompt spectra, and I discuss how these new findings can help us to discriminate between different energy dissipation mechanisms and ultimately constrain the composition of GRB jets.