Design problems, processes, and methods are topics of longstanding interest in fields such as architecture and engineering. Design tasks are also common in domains addressed by systems and management scientists. However, much scientific work in these fields indicates little awareness of design theories and research. This paper introduces systems and management scientists to the extensive design theory literature. More importantly, it consolidates and extends that literature by developing a deep conceptual analysis of design problems and problem solving. The analysis is built around five elements of design problems: goals, constraints, alternatives, representations, and solutions. These elements define the basic tasks or functional demands posed by design problem solving. The paper also identifies special difficulties faced by designers in systems and management science domains.