Sequential experiments are widely used in pharmaceutical and clinical practice. These procedures are very flexible since the experimenter can modify the trial as it goes along. A large number of them have been suggested in the literature: they correspond to different purposes of the experimenters': accurate inference, cost saving, ethical preoccupations, etc. Sequential procedures, however, pose problems as regards the correct inferential paradigm. In this presentation I give some results on the asymptotic optimality of a large class of sequential designs when the responses belong to the exponential family. In particular, for designs based on the step-by-step updating of the parameter estimates by maximum likelihood, the MLE's retain the strong consistency and asymptotic normality properties. Other results concern stopping rules and inverse sampling. A mention will be made of a special type of sequential experiments, i.e. Markovian ones: they include Biased coin Designs, Urn models, and Up-and-Down Designs.