Monocular depth estimation (MDE) is a core task in computer vision, essential for spatial understanding, 3D reconstruction, autonomous driving, and other applications. Deep learning-based MDE methods can predict relative depth from a single image, but they often lack metric information, leading to scale inconsistency and limiting their utility in downstream tasks such as visual SLAM, 3D reconstruction, and novel view synthesis. To address these limitations, monocular metric depth estimation (MMDE) has been introduced. By enabling scene-scale inference, MMDE addresses depth consistency issues, enhances temporal stability in sequential tasks, and simplifies the integration of downstream applications, significantly expanding its practical use cases. This study offers a comprehensive review of the development of depth estimation technologies, from traditional geometric approaches to modern deep learning methods, highlighting key milestones and breakthroughs in the field. Special emphasis is placed on scale-agnostic methods and their role in enabling zero-shot generalization, which has been foundational for the progress of MMDE. The study also examines the latest advancements in zero-shot MMDE, focusing on critical challenges such as improving model generalization and preserving fine edge details. To address these issues, innovative solutions have been explored, including advanced data augmentation techniques, refined model architectures, and the integration of generative approaches, leading to significant advancements. This review analyzes these solutions and their contributions in depth. The study concludes by synthesizing the connections between recent achievements in zero-shot MMDE, identifying unresolved challenges, and exploring potential future directions for research. By providing an in-depth analysis of the current state of the field and emerging trends, this study aims to serve as a valuable resource for researchers, offering a clear roadmap for understanding and advancing MMDE technology across a wide range of applications.