The Segment Anything Model (SAM) is a foundational model for image segmentation tasks, known for its strong generalization across diverse applications. However, its impressive performance comes with significant computational and resource demands, making it challenging to deploy in resource-limited environments such as mobile devices. To address this, a variety of SAM variants have been proposed to enhance efficiency without sacrificing accuracy. This survey provides the first comprehensive review of these efficient SAM variants. We begin by exploring the motivations driving this research. We then present core techniques used in SAM and model acceleration. This is followed by an in-depth analysis of various acceleration strategies, categorized by approach. Finally, we offer a unified and extensive evaluation of these methods, assessing their efficiency and accuracy on representative benchmarks, and providing a clear comparison of their overall performance.