Randomized controlled trials (RCTs) are the gold standard for assessing drug safety and efficacy. However, RCTs have some drawbacks which have led to the use of single-arm studies to make certain internal drug development and regulatory decisions, particularly in oncology. Hybrid controlled trials with real-world data (RWD), in which the control arm is composed of both trial and real-world patients, have the potential to help address some of the shortcomings of both RCTs and single-arm studies in particular situations, such as when a disease has low prevalence or when the standard of care to be used in the control arm is ineffective or highly toxic and an experimental therapy shows early promise. This paper discusses why it may be beneficial to consider hybrid controlled trials with RWD, what such a design entails, when it may be appropriate, and how to conduct the analyses. We propose a novel two-step borrowing method for the construction of hybrid control arms. We use simulations to demonstrate the operating characteristics of dynamic and static borrowing methods, and highlight the trade-offs and analytic decisions that study teams will need to address when designing a hybrid study.