In recent years, the number of crimes with weapons has grown on a large scale worldwide, mainly in locations where enforcement is lacking or possessing weapons is legal. It is necessary to combat this type of criminal activity to identify criminal behavior early and allow police and law enforcement agencies immediate action. Despite the human visual structure being highly evolved and able to process images quickly and accurately if an individual watches something very similar for a long time, there is a possibility of slowness and lack of attention. In addition, large surveillance systems with numerous equipment require a surveillance team, which increases the cost of operation. There are several solutions for automatic weapon detection based on computer vision; however, these have limited performance in challenging contexts. A systematic review of the current literature on deep learning-based weapon detection was conducted to identify the methods used, the main characteristics of the existing datasets, and the main problems in the area of automatic weapon detection. The most used models were the Faster R-CNN and the YOLO architecture. The use of realistic images and synthetic data showed improved performance. Several challenges were identified in weapon detection, such as poor lighting conditions and the difficulty of small weapon detection, the last being the most prominent. Finally, some future directions are outlined with a special focus on small weapon detection.