Disaggregated data centers (DCs) can offer high flexibility for resource allocation; hence, their resource utilization can be significantly improved. However, communications between different types of resources, in particular between CPU and memory, in fully disaggregated DCs face severe problems in terms of stringent requirements for ultra-low latency and ultra-high transmission bandwidth. Optical fiber communication is promising to provide high capacity and low latency, but it is still challenging for the state-of-the-art optical technologies to meet the requirements of fully disaggregated DCs. In this article, different levels of resource disaggregation are investigated. For fully disaggregated DCs, two architectural options are presented, where optical interconnects are necessary for the CPU-memory communications. We review the state-of-the-art optical transmission and switching technologies, and analyze pros and cons of their applicability in the disaggregated DCs. The results reveal that resource disaggregation does improve the resource utilization in DCs. However, the bandwidth provided by the state-of-the-art technologies is not always sufficient for fully disaggregated DCs. It calls for further advances in optical communications to fully utilize the advantages of fully disaggregated DCs.