This paper aims to comprehensively discuss the latest research developments in the field of underwater structural defect detection and health assessment. The underwater robots can carry the non-contact detection equipment such as optical and acoustic devices, as well as the contact-based detection equipment like ultrasonic instruments, making them important platforms for underwater structural detection methods/tools. This paper first introduces the current progress of underwater robots in the underwater structural detection, elucidating the research progress in autonomous and intelligent path planning algorithms for underwater robots. It discusses the advantages and disadvantages of non-contact defect detection methods for underwater structures based on optics and acoustics, as well as their adaptability to different detection objects and requirements. The research also investigates contact-based underwater defect detection methods and points out the limitations of such methods. It summarizes methods for the three-dimensional (3D) reconstruction using underwater images or video data, laying the foundation for precise localization and quantitative analysis of underwater structural defects. It discusses the mainstream methods for assessing the health of underwater structures, highlighting the shortcomings of existing methods. Finally, it identifies the challenges and future trends facing current underwater structural defect detection methods, providing direction for future research in the intelligent underwater structural detection and assessment.