This chapter describes the main rule-based and model-based approaches for conducting phase I dose-escalation studies with a single binary dose-limiting toxicity (DLT) endpoint. Most methods for phase I trials are based on the assumption of monotonicity; that is, if a patient has a DLT at a given dose level, then the same patient would have had a DLT had they been given a higher dose level than the one they received. The primary objective of a phase I clinical trial is to investigate the safety profile of a novel drug or drug combination and identify a tolerable dose schedule that is likely to benefit patients. Rule-based designs have long been popular with clinicians in cytotoxic drug experimentation. The 3 + 3 design is the most commonly used design in phase I clinical trials and has long been considered the routine method by clinicians for estimating the maximum tolerated dose (MTD) of novel drugs in oncology.