With the increase of artificial intelligence (AI) agents being used in the operation of digital systems, they can perform complex tasks, manage resources and interact with distributed environments. However, they require additional support in checking the execution, assigning duties and guaranteeing reliability. Therefore, it is difficult to achieve autonomous decision-making along with stable system operation. Consequently, blockchain is regarded not only as a platform for decentralized applications but also as a dependable base for AI agents. Hence, the present blockchain architectures should not only enhance their efficiency but also ensure traceable state modifications, authentic operations and coordinated communications among various AI-related activities. Therefore, our paper investigates the transaction processing and expanding methods from different perspectives. We classify the previous research into five parts: state control and security measures, improvement of sharding, scalability of consensus and Layer-2 architectures, parallel transaction processing systems and application-oriented trading procedures. For each part, we introduce some typical systems, describe their features in design and evaluate the influences on constructing scalable and trustworthy AI agent systems. Besides, we point out the difficulties in establishing the blockchain framework for AI agents. Finally, this survey presents the existing technologies systematically and highlights their importance.