Since the first methodological papers on adaptive designs, published more than 25 years ago, adaptive designs have gained increasing attention in drug development. Especially in pivotal trials, their use is subject to enhanced scrutiny by regulators as the increased complexity of flexible study designs also increases the risk of operational and statistical biases and hidden fallacies. A recent survey of Scientific Advice letters at the European Medicines Agency showed that, while the majority of adaptive design proposals were accepted or conditionally accepted, the most common concerns expressed were with respect to the control of the type I error rate, number and timing of interim analyses, bias of estimates and the insufficient justification of the adaptation strategy. Clinical trial simulations can be an important tool to learn about important properties of complex adaptive designs, especially to demonstrate for specific scenarios if the increased complexity of the adaptive approach is justified by enhanced efficiency. In the planning phase of adaptive designs, simulations are very useful to evaluate the impact of different adaptation rules, for example, on the power or average sample sizes. However, concerns have been raised if simulations can be used to "prove" type I error rate control. Especially, demonstrating type I error rate control over high dimensional parameter spaces can be computationally challenging and the complexity of simulation algorithms may be an obstacle to independent replication of simulation results.