Self-adaptive software systems adapt to changes in the environment, in the system itself, in their requirements, or in their business objectives. Typically, these systems attempt to maintain system goals at run time and often provide assurance that they will meet their goals under dynamic and uncertain circumstances. While significant research has focused on ways to engineer selfadaptive capabilities into both new and legacy software systems, less work has been conducted on how to assure that self-adaptation maintains system goals. For traditional, especially safety-critical software systems, assurance techniques decompose assurances into sub-goals and evidence that can be provided by parts of the system. Existing approaches also exist for composing assurances, in terms of composing multiple goals and composing assurances in systems of systems. While some of these techniques may be applied to self-adaptive systems, we argue that several significant challenges remain in applying them to self-adaptive systems in this chapter. We discuss how existing assurance techniques can be applied to composing and decomposing assurances for self-adaptive systems, highlight the challenges in applying them, summarize existing research to address some of these challenges, and identify gaps and opportunities to be addressed by future research 1