Abstract: Disaggregated memory (DM), as an emerging hardware architecture, has attracted extensive attention from both academia and industry in recent years. This architecture physically decouples computing and memory resources in data centers and interconnects them via high-speed networks, thereby improving resource utilization, system elasticity, and fault isolation capabilities. Distributed indexes, as the core component of memory-disaggregated storage systems, play a crucial role in efficiently organizing and maintaining data to support high-throughput, low-latency accesses for users. However, due to multiple inherent resource constraints of DM, fully exploiting the advantages of resource disaggregation to maximize index performance remains a challenging problem. This paper provides a comprehensive survey of the research progress on memory-disaggregated indexing systems. First, we introduce the fundamental features of DM and remote direct memory access (RDMA), and identify three primary challenges in constructing high-performance indexes on DM: concurrency control, read and write amplifications, and caching overhead. Subsequently, the paper categorizes existing indexing systems into three types based on their underlying data structures: hash indexes, tree indexes, and hybrid indexes. For each category, representative systems are analyzed to illustrate their design principles, implementation challenges, and key techniques. Finally, the paper highlights the main issues that require focused investigation in future research, including cross-node cooperation, fault tolerance mechanisms, and adaptation to emerging software and hardware.