Traditionally, the major objective in phase I trials is to identify a working-dose for subsequent studies, whereas the major endpoint in phase II and III trials is treatment efficacy. The dose sought is typically referred to as the maximum tolerated dose (MTD). Several statistical methodologies have been proposed to select the MTD in cancer phase I trials. In this manuscript, we focus on a Bayesian adaptive design, known as escalation with overdose control (EWOC). Several aspects of this design are discussed, including large sample properties of the sequence of doses selected in the trial, choice of prior distributions, and use of covariates. The methodology is exemplified with real-life examples of cancer phase I trials. In particular, we show in the recently completed ABR-217620 (naptumomab estafenatox) trial that omitting an important predictor of toxicity when dose assignments to cancer patients are determined results in a high percent of patients experiencing severe side effects and a significant proportion treated at sub-optimal doses.