An overview of multi-disciplinary research needs and approaches for predicting the capability of System of Systems (SoS) is provided. A SoS is a set of interconnected systems that once operated independently but have become interdependent due to revolutionary changes in demand, competition (military and otherwise) and technology. Prognosis is an assessment of capability that is made continuously as a SoS evolves and is the key to integrated health management. Fundamental research themes include: 1) hierarchical modeling of physical and human systems; 2) intelligent information gathering and management; 3) continuous simulation and experimentation; 4) prediction; and 5) decision making. The focus of the talk is on developing foresight in SoS to anticipate emergent failures. Prognosis at the component and system levels is discussed first, followed by several hypothetical examples of integrated prognostic SoS health management. Applications discussed include air/sea/land vehicle fleets in the U.S. Air Force, Navy and Army; commercial and public transportation networks; electrical power distribution grids; and product manufacturing chains.