Bayesian adaptive clinical trial designs are slowly gaining momentum in practice due to their accuracy, flexibility and efficiency in evaluating a novel drug. In this thesis, we propose novel Bayesian adaptive designs for early phase oncology trials. First, we discuss a Phase I-II trial design for therapeutic cancer vaccines and propose a two-stage approach for identifying the optimal vaccination schedule from multiple candidate vaccination schedules. We model binary outcomes for toxicity and immune response and a continuous outcome for the magnitude of immune response, conditional on a non-zero immune response. Our results suggest that incorporating more sources of information in a two-stage approach provides adequate power to identify the optimal schedule by trial completion. Next, we propose a novel Bayesian adaptive Phase I trial design that uses hierarchical modeling to share information across multiple patient populations, which may have different background standards-of-care. We propose hierarchical extensions for three models commonly used in Phase I clinical trials and propose three novel dose-finding guidelines that allow us to take full advantage of hierarchical modeling while protecting patient safety. We conclude by extending our hierarchical modeling approach to Phase I-II dose-escalation studies, where dose selection is based on both toxicity and efficacy. Our simulation results show that hierarchical modeling increases the probability of correctly identifying the maximum tolerated dose or optimal dose without increasing the rate of dose limiting toxicities. The results in this thesis are promising and motivate further research to investigate the practical challenges in implementing our proposed designs.