|Abstract:|| Response-adaptive designs are increasingly being implemented in clinical trials, particularly early phase trials, and they have increasingly stimulated the work of researchers. This paper reviews a particular class of response-adaptive designs, which have a different property from the most adaptive designs in literature. These
are response-adaptive designs targeting asymptotically the superior response, that is, treating with the superior treatment with
probability converging to one. The model underlying such designs is a randomly reinforced urn. In the context of clinical trials, this prop-
erty is particularly attractive from an ethical point of view. This overview starts from the early paper of  until the recent work by .