In this talk we will present some recent results on a posteriori error estimation for the Stokes problem. The error estimator is fully computable and present a robust and rigorous bound for the error, providing a stopping criterion for adaptive procedures, whereby elements are selectively refined where the solution is poorly resolved. The analysis is applied first to a nonconforming stable pair of elements (the Fortin-Suli element) and secondly to a wide family of conforming stabilized finite element methods. In the nonconforming case the error estimator can be constructed by taking advantage of the particularities of the Fortin-Suli element and in the conforming case the analysis is based on an equilibrated residual method which allows the application of an a posteriori selection of the stabilization parameter by a derivative free optimization procedure.