The Compute Continuum paradigm addresses the challenges of heterogeneous and dynamic computing resources, facilitating distributed application execution while enhancing data locality, performance, availability, adaptability, and energy efficiency. By integrating IoT, edge, and cloud resources into a cohesive continuum, applications can operate closer to data sources and end users. This approach supports refined adaptation strategies tailored to specific infrastructure components, enabling reduced latency, optimized bandwidth use, and improved privacy. To fully realize the Compute Continuum’s potential, autonomous and proactive management is essential, leveraging interdisciplinary methods from optimization theory, control theory, machine learning, and artificial intelligence. This special issue highlights advancements in three key areas: resource characterization and scheduling, middleware for application deployment and reconfiguration, and applications in the Compute Continuum. These contributions highlight innovative solutions for resource optimization, dynamic management, and real-world implementations, showcasing the potential of the Compute Continuum to revolutionize distributed computing across diverse domains.