With the advent of sensitive facilities like the Karl G. Jansky Very Large Array (VLA) and planning well underway for vastly more powerful wide-field interferometers like the Square Kilometer Array, the study of radio astrophysical transients is poised for dramatic growth. Radio observations provide a unique window into a wide variety of transient events, from gamma-ray bursts (GRBs) to supernovae to tidal disruption events in which a star is torn apart by a supermassive black hole. In particular, GRBs have emerged as valuable probes of some of the most extreme physics in the Universe. In these high-energy laboratories, the longer timescale of radio emission allows for extensive followup and characterization of the event energies and the densities of surrounding material. I will present our high-cadence broadband radio studies of GRB afterglows undertaken with the goal of learning more about their physical properties, the physics underlying the formation and growth of ultrarelativistic jets and outflows, and the environments in which these events occur. Our GRB radio observations reveal both intrinsic variability (reverse shocks) and extrinsic variability (interstellar scintillation).The insights derived from these studies will be invaluable for designing and interpreting the results from future radio transient surveys.