Relativistic particles interacting with their environment can produce most of the non-thermal emission we detect from the universe. However, it is still an open question how particles are accelerated to high energies and how non-thermal radiation is produced. In the present talk, we will focus on particle acceleration and radiation in blazars and galaxy clusters. Blazars are a sub-category of radio-loud active galactic nuclei with relativistic jets pointing toward the observer. They exhibit non-thermal variable emission, extending practically over the whole electromagnetic spectrum. Despite the plethora of multi-wavelength observations, the origin of the emission in blazar jets still remains an open question. We construct parametric models for studying the connection between these objects’ gamma-ray and radio emissions both in steady-state and flaring conditions and explaining the blazar phenomenology. In the second part of the talk, we will focus on particle acceleration at radio relics in galaxy clusters, which emit synchrotron radiation produced by non-thermal populations of electrons accelerated at so-called merger shocks. Low sonic Mach numbers and high beta plasma characterize these shock conditions. Here, we present an investigation of electron acceleration at merger shocks that develop multi-scale turbulence through plasma instabilities. We utilize a hybrid-kinetic numerical approach and use a recently developed energetic particle-magnetohydrodynamic (EP-MHD) code that allows us to study this system self-consistently.