A description of the conventional paradigm for early phase clinical evaluation of a new\u00a0agent is given, followed by a list of this paradigm\u2019s logical and practical flaws. This is\u00a0provided initially to motivate the use of phase I-II clinical trial designs. The main body\u00a0of the paper consists of a review of several practical Bayesian phase I-II designs for sequentially\u00a0adaptive dose-finding based on efficacy and toxicity. These include designs taking\u00a0two general approaches. The first approach uses elicited efficacy\u2013toxicity probability\u00a0pair trade-offs as decision criteria. Designs accommodating bivariate binary and trinary\u00a0outcomes are discussed, as well as an elaboration that uses patient covariates to choose\u00a0individualized doses. The second approach uses elicited joint utilities of ordinal (efficacy,\u00a0toxicity) outcomes as a decision criterion, also including adaptive randomization to improve\u00a0performance. Several illustrative applications of the methods are provided.<\/p>\n