I will present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, I will show that the system of perturbative Einstein equations reduces at each perturbation order to two (for each gravitational mode in 3 + 1 dimensions on which the talk will be focused) scalar wave equations, and then I will show how the metric perturbations can be explicitly obtained, once the solutions to these scalar wave equations are known.