Cloud computing greatly enhances the flexibility and efficiency of the utilization of computing resources by providing on-demand access to computing resources, and is widely used in various fields. However, the challenge of reasonably partitioning and dynamically adjusting these resources to improve efficiency and reduce costs has emerged. The auto-scaling mechanism, as a core function of cloud computing, can dynamically adjust resource allocation to address this issue. Currently, most survey works on auto-scaling mechanisms in cloud computing are limited to specific scenarios, and the classification of scaling strategies is often incomplete. To address these shortcomings, this paper integrates the MAPE-K loop and focuses on the three key steps of elastic scaling. It first introduces the basic concepts of cloud computing and the importance of the auto-scaling mechanism. Next, it delves into how this mechanism determines when to scale and how to accurately estimate service demand. Subsequently, the paper explores several key auto-scaling strategies, discusses their applicable scenarios, and analyzes their advantages and disadvantages. Finally, the paper identifies the challenges faced by current elastic scaling mechanisms and outlines potential future directions for development.