Time-domain astrophysics provides a unique opportunity to study the most extreme physical processes in the Universe, including the deaths of massive stars, the creation and merger of compact objects like neutron stars and black holes, and the tidal disruption of stars by supermassive black holes. I will discuss my recent and ongoing work to reveal the formation and structure of relativistic jets and outflows in the most extreme classes of astrophysical transients, including gamma-ray bursts (GRBs) and tidal disruption events (TDEs). I will further show that radio data provide the best constraints on the immediate environments of these transients, probing models of black hole growth and accretion (TDEs) and stellar evolution models (GRBs). With the pioneering detections of gravitational waves, astronomers and physicists have gained a new, complementary tool to study compact object mergers and their associated GRBs, with implications for fields as wide-ranging as general relativity, nuclear physics, cosmology, and shock physics.
