The challenges of pervasive and mobile computing environments, which are highly dynamic and unpredictable, have motivated the development of self-adaptive software systems. Although noteworthy successes have been achieved on many fronts, the construction of such systems remains significantly more challenging than traditional systems. We argue this is partially because researchers and practitioners have been struggling with the lack of a precise vocabulary for describing and reasoning about the key architectural characteristics of self-adaptive systems. Further exacerbating the situation is the fact that existing frameworks and guidelines do not provide an encompassing perspective of the different types of concerns in this setting. In this article, we present a comprehensive reference model, entitled FOrmal Reference Model for Self-adaptation (FORMS), that targets both issues. FORMS provides rigor in the manner such systems can be described and reasoned about. It consists of a small number of formally specified modeling elements that correspond to the key concerns in the design of self-adaptive software systems, and a set of relationships that guide their composition. We demonstrate FORMS's ability to precisely describe and reason about the architectural characteristics of distributed self-adaptive software systems through its application to several existing systems. FORMS's expressive power gives it a potential for documenting reusable architectural solutions (e.g., architectural patterns) to commonly encountered problems in this area.