We discuss estimation following clinical studies with Bayesian adaptive designs, including adaptive randomization, sequential stopping for futility and/or efficacy and population finding. Investigators using Bayesian designs routinely evaluate operating characteristics that report frequentist summaries of the decision problem, that is error rates and power. With the increased use of Bayesian adaptive designs it is becoming similarly important to understand the performance of estimates that are reported at the end of the trial. While from a formal Bayesian perspective posterior inference is not affected by commonly used adaptive designs, frequentist properties of the reported estimates are. We discuss related advantages and limitations of adaptive Bayesian designs and show some typical examples.