numerical relativity has undergone a revolution during the past two years, with several groups now routinely performing accurate simulations of binary black hole systems with multiple orbits, mergers, and ringdown of the holes to a final single hole equilibrium state. this talk will discuss some of the mathematical developments that made this revolution possible. in particular new insights will be discussed into how the gauge degrees of freedom may be specified in the einstein equations, and how this changes the behavior of the constraints of the theory.