The behavior of terrorist groups may seem highly strategic and thus largely contingent (unpredictable), however, by taking a comparative approach in considering data on terrorist attacks, we find that surprising patterns emerge. In this talk, Ill describe recent work on discovering and understanding the structure of terrorist attacks over the past 40 years, and in particular the regular behavior of terrorist organizations. These results shed new light on the origin of severe terrorist attacks and point to fundamental constraints on the dynamics of terrorism.