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This dissertation develops new methods for unaddressed issues in the design of Bayesian adaptive Phase I and Phase I/II oncology clinical trials, which are trials that seek to identify the optimal dose and/or schedule of a new cytotoxic agent in a small group of patients either based on dose-limiting toxicity (DLT) alone or both toxicity and efficacy. Our first project focuses on methods to calibrate the prior variance assumed for the parameter in the Continual Reassessment Method (CRM). We propose three systematic approaches to adaptively calibrate the prior variance continually throughout the trial and compare those approaches to existing methods that calibrate the variance only at the beginning of a trial. Computer simulations show that our approaches have the ability to perform better than the existing methods under various scenarios. In our second project, we extend the traditional Phase I dose-schedule-finding design that only optimizes dose and schedule among patients by adaptively re-evaluating and, if necessary, varying the intra-patient dose-schedule assignment as the study proceeds. Our design is based on a Bayesian non-mixture cure rate model that incorporates multiple administrations each patient receives with the per-administration dose included as a covariate. Simulations indicate that our design identifies correct dose and schedule combinations as well as the traditional method that does not allow for intra-patient doses-schedule reassignments, but with a larger number of patients assigned to those combinations. The method is illustrated by application to a bone marrow transplantation trial for acute myelogenous leukemia (AML). In our third project, we generalize our method in the second project by jointly modeling toxicity and efficacy as time-to-event outcomes in a Phase I/II clinical trial. We adopt a non-mixture cure rate model for the marginal distributions. A copula is then assumed to obtain a bivariate time-to-event distribution. To ensure an ethical trial, dose-schedule regimes are selected for successive patient cohorts based on the proposed safety and efficacy acceptability criteria at each decision-making time. Through simulations we show that the proposed design has a high probability of making correct decisions and treats most patients at desirable treatment regimes.