Stars in the immediate vicinity of supermassive black holes (SMBHs) can be ripped apart by the tidal forces of the black hole. The subsequent accretion of the stellar material causes a spectacular flare of electromagnetic radiation. Here, we provide a review of the observations of tidal disruption events (TDEs), with an emphasis on the important contributions of Swift to this field. TDEs represent a new probe of matter under strong gravity, and have opened up a new window into studying accretion physics under extreme conditions. The events probe relativistic effects, provide a new means of measuring black hole spin, and represent signposts of intermediate-mass BHs, binary BHs and recoiling BHs. Luminous, high-amplitude X-ray flares, matching key predictions of the tidal disruption scenario, have first been discovered with ROSAT, and more recently with other missions and in other wavebands. The Swift discovery of two gamma-ray emitting, jetted TDEs, never seen before, has provided us with a unique probe of the early phases of jet formation and evolution, and SwiftJ1644+75 has the best covered lightcurve of any TDE to date. Further, Swift has made important contributions in providing well-covered lightcurves of TDEs discovered with other instruments, setting constraints on the physics that govern the TDE evolution, and including the discovery of the first candidate binary SMBH identified from a TDE lightcurve.