Automation of the execution of computational tasks is at the heart of improving scientific productivity. Over the last years, scientific workflows have been established as an important abstraction that captures data processing and computation of large and complex scientific applications. By allowing scientists to model and express entire data processing steps and their dependencies, workflow management systems relieve scientists from the details of an application and manage its execution on a computational infrastructure. As the resource requirements of today’s computational and data science applications that process vast amounts of data keep increasing, there is a compelling case for a new generation of advances in high-performance computing, commonly termed as extreme-scale computing, which will bring forth multiple challenges for the design of workflow applications and management systems. This paper presents a novel characterization of workflow management systems using features commonly associated with extreme-scale computing applications. We classify 15 popular workflow management systems in terms of workflow execution models, heterogeneous computing environments, and data access methods. The paper also surveys workflow applications and identifies gaps for future research on the road to extreme-scale workflows and management systems.