Adaptivity is a key concept for the effective numerical solution of differential equations. The multilevel solution of elliptic partial differential equations can be combined with adaptive mesh refinement and an adaptive choice of the discretization order. Additionally, adaptivity may be built into the relaxation and the multilevel cycling strategy. The goal of these fully adaptive methods is to spend work only where it is most effective in the solution process. This approach includes concepts like local relaxation and not only leads to particularly fast convergence but also to additional robustness and generality. The efficient implementation of fully adaptive multilevel methods in a finite element framework will be discussed.