Web services are a consolidated reality of the modern Web with tremendous, increasing impact on everyday computing tasks. They turned the Web into the largest, most accepted, and most vivid distributed computing platform ever. Yet, the use and integration of Web services into composite services or applications, which is a highly sensible and conceptually non-trivial task, is still not unleashing its full magnitude of power. A consolidated analysis framework that advances the fundamental understanding of Web service composition building blocks in terms of concepts, models, languages, productivity support techniques, and tools is required. This framework is necessary to enable effective exploration, understanding, assessing, comparing, and selecting service composition models, languages, techniques, platforms, and tools. This article establishes such a framework and reviews the state of the art in service composition from an unprecedented, holistic perspective.