Multi-object tracking is an important branch in the field of computer vision. Owing to the rapid development of computer hardware and deep learning technology, significant progress has been made in deep learning-based multi-object tracking, yielding remarkable results. To promote the research progress in the field of visual multi-object tracking, a comprehensive review of recent innovative outcomes was conducted to discuss the current state of research advancements. On the basis of introducing the background and application scenarios of multi-object tracking, the research progress was discussed in four aspects: tracking by detection, joint detecting and tracking, transformer-based tracking, referring multi-object tracking. Common benchmark datasets and evaluation metrics for multi-tracking algorithms were summarized, and a comparative analysis of the algorithms mentioned was conducted on these datasets. Ultimately, exploring the prospective evolution of deep learning-based visual multi-object tracking, three future research directions were proposed for scholars actively engaged in this field.