Abstract: The exponential growth of constraint violations is one of the most urgent problems facing the numerical relativity community today. These constraint violations cause most numerical solutions of the Einstein evolution equations quickly to become unphysical and large (and then to crash the code). I will describe several recent advances by the Caltech numerical relativity group in controlling the growth of these constraints, including the results of some 3D non-linear numerical tests of these ideas for dynamical black-hole spacetimes. These new constraint control ideas include constraint preserving boundary conditions, optimal constraint projection, and some new constraint suppressing forms of the evolution equations.