Response-adaptive designs, or response-adaptive randomization procedures, are designs that change allocation away from 50/50 based on responses observed so far in the trial. The desired allocation proportion is usually motivated by an ethical consideration of assigning more patients to better treatments. This review presents several classes of response-adaptive designs, and discusses the advantages and disadvantages of these designs, and the analysis of clinical trials based on adaptive designs. We also discuss goals for the allocation proportion and the power of treatment comparison in the trial where response-adaptive design is used.