Adaptive finite element methods have been used for the solution of linear and non-linear elliptic partial differential equations since the 70s. However, only recently have rigorous convergence and (even stronger) contraction results been developed for a large class of interesting problems. In this talk, the basic adaptive finite element framework will be presented along with an overview of some convergence results. Also, a new efficient, reliable, and robust error estimator for problems in three dimensions will be presented along with numerical computations supporting its use.