Abstract: Crowd counting, aiming to estimate the number, density or distribution of crowds in images or videos, belongs to the research category of object counting. It has been widely employed in crowd behavior analysis and public safety management to detect crowding or abnormal behavior in time to avoid accidents. In the past decades, although tremendous efforts have been made to enhance the performance of crowd counting algorithms, some long-standing challenges, such as cross-scene counting, perspective distortion and scale variation, remain unresolved. Along this line, an emerging research trend is to exploit the deep learning technologies for crowd counting. It has been proven to be an effective way to address the above issues. In this paper, crowd counting models based on deep learning are reviewed, analyzed, and discussed. Firstly, crowd counting models are introduced in details from the perspective of their principles, steps, and model variants, and the difference between the crowd counting models based on traditional methods and the crowd counting models based on deep learning are analyzed. Then the research status of crowd counting based on deep learning are expounded from four aspects: network structure, ground-truth generation, loss function and evaluation index. Meanwhile, the characteristics of various crowd counting data sets are compared and analyzed. Finally, some future directions of crowd counting are given.