AI agents are evolving from isolated task executors into networked autonomous entities that can communicate, delegate tasks, invoke tools, access external knowledge, and participate in cross-platform service and economic workflows. This evolution gives rise to open agent networks, where heterogeneous agents owned by different stakeholders interact without naturally shared infrastructures for identity, authorization, auditability, reputation, or settlement. This survey and tutorial article reviews the literature over the period 1980--2026 on the evolution from classical multi-agent systems to open agent networks, with a particular focus on LLM-based autonomous agents, agent interoperability protocols, Internet-of-Agents infrastructures, and blockchain-enabled trust mechanisms. We first review this evolution and show how the trust boundary expands from individual execution to cross-agent, cross-platform, and cross-organizational interaction. We then identify a network-level trust crisis that cannot be fully addressed by single-agent safety mechanisms or closed multi-agent coordination techniques, and develop a five-dimensional taxonomy covering entity and capability trust, authorization and delegation trust, information and provenance trust, coordination and group-robustness trust, and accountability and settlement trust. Based on this taxonomy, we examine how blockchain can provide shared identity, verifiable authorization, tamper-evident provenance, auditable collaboration, incentive alignment, and value settlement for trustworthy agent networks. We further synthesize the mapping between agent-network risks, trust requirements, and blockchain-enabled mechanisms, and clarify the role of blockchain as a shared trust layer rather than a replacement for agent security, semantic verification, privacy protection, or robust reasoning.

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