IBM Research is engaged in a research program in symbiotic cognitive computing to investigate how to embed cognitive computing in physical spaces. This article proposes five key principles of symbiotic cognitive computing: context, connection, representation, modularity, and adaptation, along with the requirements that flow from these principles. We describe how these principles are applied in a particular symbiotic cognitive computing environment and in an illustrative application for strategic decision making. Our results suggest that these principles and the associated software architecture provide a solid foundation for building applications where people and intelligent agents work together in a shared physical and computational environment. We conclude with a list of challenges that lie ahead.