The rise of large language model (LLM)-powered agents is transforming services computing, moving it beyond static, request-driven functions toward dynamic, goal-oriented, and socially embedded multi-agent ecosystems. We propose Agentic Services Computing (ASC), a paradigm that reimagines services as autonomous, adaptive, and collaborative agents capable of perceiving, reasoning, acting, and evolving in open and uncertain environments. We organize ASC around a four-phase lifecycle: Design, Deployment, Operation, and Evolution. It is examined through four interwoven research dimensions: (i) perception and context modeling, (ii) autonomous decision-making, (iii) multi-agent collaboration, and (iv) evaluation with alignment and trustworthiness. Rather than functioning as isolated layers, these dimensions evolve together. Contextual grounding supports robust deployment; autonomous reasoning drives real-time action; collaboration emerges from agent interaction; and trustworthiness is maintained as a lifelong, cross-cutting commitment across all lifecycle stages. In developing this framework, we also survey a broad spectrum of representative works that instantiate these ideas across academia and industry, mapping key advances to each phase and dimension of ASC. By integrating foundational principles of services computing with cutting-edge advances in LLM-based agency, ASC offers a unified and forward-looking foundation for building intelligent, accountable, and human-centered service ecosystems.
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