Underwater marine object detection, as one of the most fundamental techniques in marine engineering, has been shown to exhibit significant potential for exploring underwater environment in recent years. It has been applied widely in the monitoring of underwater ecosystems, exploration of natural resources, management of commercial fishery management, and other areas. However, due to the complexity of underwater environment, characteristics of marine object, and limitation from exploration equipment, the detection performance revolving around speed, accuracy and robustness could be degraded dramatically. In this context, we present a survey of deep-learning-based underwater marine object detection. To facilitate comprehensive understanding of the subject matter, we categorize the existing research challenges of underwater object detection into image quality degradation, small object detection, poor generalization and real-time detection. Corresponding to each category of the existing challenges, we review recent advances and highlight the pros and cons of existing techniques. Furthermore, we give a detailed and critical review of the most widely used benchmark datasets for underwater marine object detection. Comparisons with existing reviews and future trends of the subject matter, particularly AI-based techniques, are also presented.