The colours of the extreme universe

This thesis presents pioneering work on the panchromatic emission of some of the most luminous galaxies in the early Universe: star forming galaxies and active galactic nuclei. Using state-of-the-art statistical methods and new-generation radio-to-X-rays instruments, this thesis expands the parameter space covered by current multi-wavelength studies of galaxy evolution. In particular, this thesis pushes three different frontiers. The statistical frontier is explored by developing a sophisticated statistical tool to robustly recover the parameters required to model multi-wavelength emission. The wavelength frontier is pushed forward by exploring galaxy evolution from the new spectral window at low-frequency radio, opened by the LOFAR instrument. Finally, the resolution frontier will be pushed by exploring the distribution of emission components across the spectrum using a combination of high-resolution ALMA and HST imaging.