Abstract: Although the non-thermal component of the ICM has a relatively low energy density, it can still exert a profound influence. Turbulence provides pressure support, affects magnetic field topology and thus thermal conduction, and is a source of dissipation, heat and metal diffusion. Cosmic-rays likewise provide pressure support and heating, and contain archaeological information about cosmological shocks and AGN activity, which can be mined in radio and gamma-ray data. We discuss several aspects. Turbulence: we develop a novel spectral analysis technique for Astro-H which exploits not just the line width but the entire line shape, and show how the excellent spectral resolution of Astro-H can overcome its relatively poor spatial resolution in making detailed inferences about the ICM velocity field. Cosmic rays: we show how super-Alfvenic streaming of cosmic rays can turn off radio halos, potentially explaining the observed bimodality in radio halo luminosity. We also show how diffusive shock acceleration in previous structure formation shocks can leave behind a fossil a^1/4 MeV electron population in the cluster outskirts, in the face of loss processes. Relic reacceleration can dominate over fresh injection at low Mach numbers, allowing weak shocks which would would be otherwise invisible to glow in radio emission, potentially visible with LOFAR.