A crucial task in marine research is that of monitoring fish in order to quantify different species and analyze their behavior. Computer Vision clearly helps in solving this problem, especially when combined with Deep Learning. This paper focuses on the use of Deep Learning and Computer Vision to perform fish detection and tracking. More specifically, in this study we survey different state-of-the-art object detectors, we adapt and train them to perform fish detection, and we evaluate and compare them by means of a large underwater video sequence involving fish in their natural habitat. The experimental results, provided in terms of detection quality and time consumption, will help researchers to choose the appropriate object detection model depending on the pursued goals.