A description of the conventional paradigm for early phase clinical evaluation of a new agent is given, followed by a list of this paradigm’s logical and practical flaws. This is provided initially to motivate the use of phase I-II clinical trial designs. The main body of the paper consists of a review of several practical Bayesian phase I-II designs for sequentially adaptive dose-finding based on efficacy and toxicity. These include designs taking two general approaches. The first approach uses elicited efficacy–toxicity probability pair trade-offs as decision criteria. Designs accommodating bivariate binary and trinary outcomes are discussed, as well as an elaboration that uses patient covariates to choose individualized doses. The second approach uses elicited joint utilities of ordinal (efficacy, toxicity) outcomes as a decision criterion, also including adaptive randomization to improve performance. Several illustrative applications of the methods are provided.