The recent spurt in the development of cloud-native applications, microservices, and edge computing has generated an immediate necessity regarding more accurate and flexible strategies to manage resources. The conventional coarse-grained techniques have difficulty in satisfying the dynamic, heterogeneous, and performance-sensitive requirements of the current distributed systems, which results in inefficiencies, bottlenecks, and elevated costs of operations.This research summarizes the current developments in Fine-Grained Resource Allocation (FGRA) in a microservice-based cloud computing environment, where the novel techniques should utilize genetic algorithms, microservice disaggregation,graph-based partitioning, search-tree access control, and cloud-edge orchestration technology. The poll also shows how new methods enhance resource use, minimize execution time, scale,and provide intelligent and tailored service deployment on a wide range of cloud deployment. Further stress is put on the factors of workload fluctuation, infrastructure heterogeneity,and changing service requirements on the efficiency of FGRA methods under real-life conditions. In general, the review shows that FGRA is important to optimize the work of microservices,support real-time service requirements, and facilitate efficient and resilient cloud-edge ecosystems needed by next-generation distributed application