The concept of the Web of Agents (WoA), which transforms the static, document-centric Web into an environment of autonomous agents acting on users' behalf, has attracted growing interest as large language models (LLMs) become more capable. However, research in this area is still fragmented across different communities. Contemporary surveys catalog the latest LLM-powered frameworks, while the rich histories of Multi-Agent Systems (MAS) and the Semantic Web are often treated as separate, legacy domains. This fragmentation obscures the intellectual lineage of modern systems and hinders a holistic understanding of the field's trajectory. We present the first comprehensive evolutionary overview of the WoA. We show that modern protocols like A2A and the MCP, are direct evolutionary responses to the well-documented limitations of earlier standards like FIPA standards and OWL-based semantic agents. To systematize this analysis, we introduce a four-axis taxonomy (semantic foundation, communication paradigm, locus of intelligence, discovery mechanism). This framework provides a unified analytical lens for comparing agent architectures across all generations, revealing a clear line of descent where others have seen a disconnect. Our analysis identifies a paradigm shift in the 'locus of intelligence': from being encoded in external data (Semantic Web) or the platform (MAS) to being embedded within the agent's core model (LLM). This shift is foundational to modern Agentic AI, enabling the scalable and adaptive systems the WoA has long envisioned. We conclude that while new protocols are essential, they are insufficient for building a robust, open, trustworthy ecosystem. Finally, we argue that the next research frontier lies in solving persistent socio-technical challenges, and we map out a new agenda focused on decentralized identity, economic models, security, and governance for the emerging WoA.