Visual Simultaneous Localization and Mapping (VSLAM) has been a hot topic of research since the 1990s, first based on traditional computer vision and recognition techniques and later on deep learning models. Although the implementation of VSLAM methods is far from perfect and complete, recent research in deep learning has yielded promising results for applications such as autonomous driving and navigation, service robots, virtual and augmented reality, and pose estimation. The pipeline of traditional VSLAM methods based on classical image processing algorithms consists of six main steps, including initialization (data acquisition), feature extraction, feature matching, pose estimation, map construction, and loop closure. Since 2017, deep learning has changed this approach from individual steps to implementation as a whole. Currently, three ways are developing with varying degrees of integration of deep learning into traditional VSLAM systems: (1) adding auxiliary modules based on deep learning, (2) replacing the original modules of traditional VSLAM with deep learning modules, and (3) replacing the traditional VSLAM system with end-to-end deep neural networks. The first way is the most elaborate and includes multiple algorithms. The other two are in the early stages of development due to complex requirements and criteria. The available datasets with multi-modal data are also of interest. The discussed challenges, advantages, and disadvantages underlie future VSLAM trends, guiding subsequent directions of research.