Optical endoscopy has become an essential diagnostic and therapeutic approach in modern biomedicine for directly observing organs and tissues deep inside the human body, enabling non-invasive, rapid diagnosis and treatment. Optical fiber endoscopy is highly competitive among various endoscopic imaging techniques due to its high flexibility, compact structure, excellent resolution, and resistance to electromagnetic interference. Over the past decade, endoscopes based on a single multimode optical fiber (MMF) have attracted widespread research interest due to their potential to significantly reduce the footprint of optical fiber endoscopes and enhance imaging capabilities. In comparison with other imaging principles of MMF endoscopes, the scanning imaging method based on the wavefront shaping technique is highly developed and provides benefits including excellent imaging contrast, broad applicability to complex imaging scenarios, and good compatibility with various well-established scanning imaging modalities. In this review, various technical routes to achieve light focusing through MMF and procedures to conduct the scanning imaging of MMF endoscopes are introduced. The advancements in imaging performance enhancements, integrations of various imaging modalities with MMF scanning endoscopes, and applications are summarized. Challenges specific to this endoscopic imaging technology are analyzed, and potential remedies and avenues for future developments are discussed.