This thesis presents the implications of using adaptive time-stepping schemes with the adjoint-state method, a widely used algorithm for computing derivatives in optimal-control problems. Though we gain control over the accuracy of the timestepping scheme, the forward and adjoint time grids become mismatched. Despite this fact, I claim using adaptive time-stepping for optimal control problems is advantageous for two reasons. First, taking variable time-steps potentially reduces the computational cost and improves accuracy of the forward and adjoint equations' numerical solution. Second, by appropriately adjusting the tolerances of the timestepping scheme, convergence of the optimal control problem can be theoretically guaranteed via inexact Newton theory. I present proofs and computational results to support this claim.