The core of the multilevel adaptive iterative method consists of a relaxation scheme and an active set strategy. The active set is used to monitor where the iteration efficiently reduces the error. It is incrementally updated exploiting the current solution and the matrix structure. Arithmetic operations are restricted to the active set. The concept can be extended to a multilevel structure by additionally tracing the dependencies between unknowns on different levels. It improves the robustness and efficiency of classical multilevel methods; in particular it is an almost ideal supplement of adaptive refinement techniques.