We discuss some of the statistical approaches to the design and analysis of phase I clinical trials in cancer. An attempt is made to identify the issues, particular to this type of trial, that should be addressed by an appropriate methodology. A brief review of schemes currently in use is provided together with our views of the extent to which any particular scheme addresses the main issues. Some simulations are provided together with graphical illustration of the operating characteristics of the particular methods. It appears that the continual reassessment method is preferable to other contending schemes.