Exotic Transients: From Discovery to Multi-Wavelength Characterization

Time-domain surveys are finding tens of thousands (and soon millions) of transient events.  But how do we make new discoveries of rare and exotic events? And how do we figure out what causes and powers them? I will discuss several approaches that have successfully uncovered new rare classes of transients, revealed new and unpredicted physical processes, and have led to a deeper understanding of progenitors at the population-level.  I will draw examples from our recent work on superluminous supernovae, tidal disruption events and their unexpected late radio emission, and a new population of decade-long transients that is still being deciphered.