A number of designs of phase I dose-finding trials have been developed. Algorithm-based designs such as standard 3 + 3 designs are easy to understand and implement since they do not require explicit model specification for a dose-toxicity relationship. On the other hand, model-based designs such as the continual reassessment method (CRM) (O’Quigley et al., 1990) have been proposed. The author will give a review of the CRM and its related topics. In particular, the author makes mention of some of the problems with 3 + 3 designs that have often been used in phase I dose-finding studies and gives a detailed description of ideas, concepts, theories, properties and issues in the CRM.