As transient surveys grow wider and faster, and followup facilities become more automated and global, we are able to discover and characterize events in new parts of phase space. Among these are new classes of rapidly evolving supernovae, which challenge our most basic models of explosion powering mechanisms; new types of accretion events onto supermassive black holes, which can provide novel clues into the formation of these objects; and the very rapidly evolving emission from the GW170817 binary neutron-star merger, which can teach us about physics from the nuclear equation of state to cosmology. I will discuss what we have learned from these events so far, and what kinds of tools we have, and are building, to gain even more insights from them in the future.