Effective multigrid performance results from smoothing and coarse-grid correction working together as complementary processes. Coarse-grid correction is designed to capture those components of the error not effectively dampened by relaxation. Adaptive or self-correcting multigrid methods exploit information produced by cycling to uncover algebraically smooth error and adjust the multigrid components as needed in order to improve the rate toward convergence. This talk reviews the adaptive multigrid via subcycling on complementary grids method. It also discusses the effectiveness of this method as a preconditioner for conjugate gradient - where conjugate gradient is and is not included in the adaptive setup stage. Numerical results are included.