Advances in large language models have enabled agentic AI systems that can reason, plan, and interact with external tools to execute multi-step workflows, while public blockchains have evolved into a programmable substrate for value transfer, access control, and verifiable state transitions. Their convergence introduces a high-stakes systems challenge: designing standard, interoperable, and secure interfaces that allow agents to observe on-chain state, formulate transaction intents, and authorize execution without exposing users, protocols, or organizations to unacceptable security, governance, or economic risks. This survey systematizes the emerging landscape of agent-blockchain interoperability through a systematic literature review, identifying 317 relevant works from an initial pool of over 3000 records. We contribute a five-part taxonomy of integration patterns spanning read-only analytics, simulation and intent generation, delegated execution, autonomous signing, and multi-agent workflows; a threat model tailored to agent-driven transaction pipelines that captures risks ranging from prompt injection and policy misuse to key compromise, adversarial execution dynamics, and multi-agent collusion; and a comparative capability matrix analyzing more than 20 representative systems across 13 dimensions, including custody models, permissioning, policy enforcement, observability, and recovery. Building on the gaps revealed by this analysis, we outline a research roadmap centered on two interface abstractions: a Transaction Intent Schema for portable and unambiguous goal specification, and a Policy Decision Record for auditable, verifiable policy enforcement across execution environments. We conclude by proposing a reproducible evaluation suite and benchmarks for assessing the safety, reliability, and economic robustness of agent-mediated on-chain execution.