As cloud computing usage grows, cloud data centers play an increasingly important role. To maximize resource utilization, ensure service quality, and enhance system performance, it is crucial to allocate tasks and manage performance effectively. The purpose of this study is to provide an extensive analysis of task allocation and performance management techniques employed in cloud data centers. The aim is to systematically categorize and organize previous research by identifying the cloud computing methodologies, categories, and gaps. A literature review was conducted, which included the analysis of 463 task allocations and 480 performance management papers. The review revealed three task allocation research topics and seven performance management methods. Task allocation research areas are resource allocation, load-Balancing, and scheduling. Performance management includes monitoring and control, power and energy management, resource utilization optimization, quality of service management, fault management, virtual machine management, and network management. The study proposes new techniques to enhance cloud computing work allocation and performance management. Short-comings in each approach can guide future research. The research's findings on cloud data center task allocation and performance management can assist academics, practitioners, and cloud service providers in optimizing their systems for dependability, cost-effectiveness, and scalability. Innovative methodologies can steer future research to fill gaps in the literature.