We review the rationale behind the statistical design of dose-finding studies as used in phase I and phase I/II clinical trials. We underline what the objectives of such dose-finding studies should be and why the widely used standard design fails to meet any of these objectives. The standard design is a "memoryless" design and we discuss how this impacts on practical behaviour. Designs introduced over the last two decades can be viewed as designs with memory and we discuss how these designs are superior to memoryless designs. By superior we mean that they require less patients overall, less patients to attain the maximum tolerated dose (MTD), and concentrate a higher percentage of patients at and near to the MTD. We reanalyse some recently published studies in order to provide support to our contention that markedly better results could have been achieved had a design with memory been used instead of a memoryless design.