Since the 1960s, Galactic neutron stars have been known to emit short duration radio transients. More recently, a population of higher luminosity short-duration radio transients originating from extragalactic distances were discovered. The nature of these fast radio bursts (FRBs) still remains a mystery, but it is clear that they reflect an extreme astrophysical process, too extreme to be replicated on Earth. Additionally, these transients carry valuable clues about otherwise invisible material that they pass through on their journey to Earth. Currently FRBs are divided into two groups observationally: those which repeat and those which have been seen only a single time. In this thesis, we probe FRB burst properties and their local environments at the highest possible resolutions, to address the following open science questions: what types of astrophysical objects are capable of producing FRB emission?; do repeating and non-repeating FRBs have the same physical origin?; are all repeating FRBs the same type of object?; and what is the physical mechanism creating these luminous radio transients? We show that FRBs come in a variety of “shapes and sizes” in their timescales, luminosities and local environments. This diversity must be accommodated for in the progenitor and emission models of fast radio transients: either a single FRB progenitor exists that can live in a large variety of surroundings, or FRBs can originate from multiple astrophysical sources.