We will study the high-energy face of some of the densest astrophysical environments including starbursting galaxies and the molecular material suffusing our own Galactic centre. Recent exciting observations by a new generation of astronomical instruments reveal that this region of the Galaxy is permeated by high-energy particles and photons (possibly energised by the supermassive black hole that sits at the very centre of the Milky Way) and intense magnetic fields. Our theoretical study will uncover the interactions between these players and the impacts they have on the overall dynamics of the Galactic centre region. Our work will uncover the parallels between this relatively local environment and the ultra-dense and ultra-energetic environs of star-bursting galaxies. We will also explore the relationship between gamma-ray and radio signals detected from the same astrophysical regions (like the molecular matter in the Galactic centre) and consider how these two might be inter-related through the phenomenon of hadronic cosmic ray collisions with ambient gas. The promise of these simultaneously-detected signals (from photons differing in energy by around eighteen orders of magnitude) to reveal details of magnetic field structure and amplitude will be explored.