We propose a hierarchical framework for collaborative intelligent systems. This framework organizes research challenges based on the nature of the collaborative activity and the information that must be shared, with each level building on capabilities provided by lower levels. We review research paradigms at each level, with a description of classical engineering-based approaches and modern alternatives based on machine learning, illustrated with a running example using a hypothetical personal service robot. We discuss cross-cutting issues that occur at all levels, focusing on the problem of communicating and sharing comprehension, the role of explanation and the social nature of collaboration. We conclude with a summary of research challenges and a discussion of the potential for economic and societal impact provided by technologies that enhance human abilities and empower people and society through collaboration with intelligent systems.