Monocular depth estimation (MDE), as one of the fundamental tasks of computer vision, plays important roles in downstream applications such as virtual reality, 3D reconstruction, and robotic navigation. Convolutional neural networks (CNN)-based methods gained remarkable progress compared with traditional methods using visual cues. However, recent researches reveal that the performance of MDE using CNN could be degraded due to the local receptive field of CNN. To bridge the gap, various attention mechanisms were proposed to model the long-range dependency. Although reviews of MDE algorithms based on CNN were reported, a comprehensive outline of how attention boosts MDE performance is not explored yet. In this paper, we firstly categorize recent attention-related works into CNN-based, Transformer-based, and hybrid (CNN–Transformer-based) approaches in the light of how the attention mechanism impacts the extraction of global features. Secondly, we discuss the details and contributions of attention-based MDE methods published from 2020 to 2022. Then, we compare the performance of the typical attention-based methods. Finally, the challenges and trends of the attention mechanism used in MDE are discussed.