The centers of galaxies feature the densest stellar environments in the Universe.  In the gravitational blender of a galactic nucleus, close encounters between stars and compact objects that would never happen elsewhere in the Universe occur with regularity, and lead to a variety of transients in electromagnetic and gravitational wave radiation.  In this talk, I will give a detailed overview of one particular type of electromagnetic transient: stellar tidal disruption events, or TDEs.  TDEs occur when unlucky stars wander too close to supermassive black holes (SMBHs).  Long predicted by theorists, TDEs are now discovered by observers at a rate of dozens per year thanks to the last decade's advances in time domain astronomy.  In the near future, the launch of Israel's ULTRASAT mission will make it possible to find thousands of TDEs per year.  I will describe how TDEs can be used to measure SMBH masses and spins, to discover elusive "intermediate-mass" black holes, and to resolve long-standing questions on the origins and evolution of massive black holes over cosmic time.  I will also briefly mention the other types of transients that can be produced in galactic nuclei, with a focus on gravitational waves.