Dose escalation in phase I studies is generally performed on the basis of clinical experience and judgement. In this paper some of the statistical approaches that have been proposed for the formalization of the procedure are described. Apart from the use of the Continual Reassessment Method in oncology studies, such formal methods have received little implementation. The purpose of presenting them here is to promote their further exploration and appropriate implementation. Certain limitations are discussed, which will be best overcome by collaboration between clinical pharmacologists and statisticians.