Advanced polymer matrix composites (PMC) have many advantages such as light weight and high specific strength that make them useful for many aerospace applications. Enormous uncertainty exists, however, in predicting long-term changes in properties of PMCs under extreme environmental conditions, which has limited their use. To help address this issue, the Department of Defense requested a study from the NRC to identify the barriers and limitations to the use of PMCs in extreme environments. The study was to focus on issues surrounding methodologies for predicting long-term performance. This report provides a review of the challenges facing application of PMCs in extreme environments, the current understanding of PMC properties and behavior, an analysis of the importance of data in developing effective models, and recommendations for improving long-term predictive methodologies.