OBJECTIVES: Single arm trial designs are often used in clinical development in cases where randomisation to a comparator is practically or ethically not possible. More specifically for three-outcome one-stage designs or for adaptive designs, Bayesian data analysis can be useful or even a required alternative. This work will summarize the main statistical concepts of Bayesian analysis of single arms studies and highlights the role of historical data in such cases. METHODS: Two recent real-world examples will be presented: 1) In the HIV area, a case of Bayesian adaptive phase 3 study designed as a single-arm trial due to ethical and patients accrual constrains. In this case, Bayesian decision rules for concluding at interim and final analyses were defined a priori. Historical control was derived from a meta-analysis of previous trials. 2) In prostate cancer, a case of three-outcome one-stage design was planned with a final decision rule based on a frequentist test of the null hypothesis and assuming a pre-defined sample size. A post hoc Bayesian re-analysis was proposed to leverage all the data actually collected in the trial using Bayes factors (BF) to compare hypotheses. In both cases, non-informative priors were used. RESULTS: In the HIV example, the Bayesian adaptive scheme resulted in a division by 2 of the expected study size and duration as compared to a classical single-arm trial. In the prostate cancer example, the Bayes factor corresponding to the decision rule of the three-outcome test was evaluated to be BF=16. Bayesian data re-analysis using all data collected showed that BF=13 hence allowing the null hypothesis rejection, while strictly applying the predefined frequentist rule could not. Both cases led to successful regulatory submissions. CONCLUSIONS: Bayesian design and analysis of single arm studies can increase the power of an analysis and strengthen post hoc analyses even when using non-informative priors.