The rapid evolution of cloud computing has introduced a multitude of challenges related to resource allocation, task scheduling, and overall system efficiency. Among the various computational problems addressed within cloud environments, Bin Packing Problems (BPP) have emerged as a pivotal area of study. This work provides a comprehensive review of the models and strategies that leverage BPP to tackle diverse challenges and objectives in cloud computing. We explore the application of BPP in optimizing resource utilization, reducing energy consumption, enhancing load balancing, and improving the overall performance of cloud infrastructures. Our analysis begins with an overview of traditional BPP formulations and their relevance to cloud computing. We then delve into advanced BPP models tailored for dynamic and heterogeneous cloud environments, highlighting their adaptability to varying workload patterns and resource demands. We also examine heuristic and metaheuristic approaches that have been employed to solve complex cloud instances, offering a comparative analysis of their effectiveness in real-world cloud scenarios. Furthermore, case studies are presented to illustrate successful implementations of BPP strategies in cloud service providers, demonstrating significant improvements in operational efficiency and cost savings. This paper underscores the importance of BPP in advancing cloud computing technologies, providing insights into future research directions and potential applications. By bridging the gap between theoretical models and practical implementations, we aim to contribute to the ongoing development of robust, efficient, and scalable cloud systems.