The rise of LLM-powered agents is driving a fundamental transformation in services computing: from static, request-response functions to dynamic, goal-oriented, and autonomous multi-agent ecosystems. In response to this shift, we introduce Agentic Service Computing (ASC), a new paradigm that reimagines services as intelligent, self-adaptive, and socially embedded entities. This comprehensive survey presents a lifecycle-driven framework for ASC, structured around four core phases: Design, Deployment, Operation, and Evolution. We systematically analyze ASC through four foundational research dimensions: (1) Perception, Context, and Environment Modeling, (2) Autonomous Decision-Making and Task Execution, (3) Multi-Agent Collaboration and Organization, and (4) Evaluation, Value Alignment, and Trustworthiness. We examine how these dimensions are instantiated, integrated, and continuously adapted across the service lifecycle. Our synthesis reveals that agentic services are not merely assembled but orchestrated: contextual awareness enables robust deployment; autonomous reasoning supports real-time operation; collaborative structures emerge and evolve through interaction; and trustworthiness must be upheld as a cross-cutting, lifelong imperative. We further identify and discuss emerging trends shaping the future of ASC. By integrating classical principles of services computing with advances in LLM-based multi-agent systems, this work establishes a holistic and forward-looking foundation for ASC. It provides a unified reference for researchers and practitioners aiming to develop adaptive, accountable, and human-centered intelligent services.

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