In recent times, the utilisation of marine composites in tubular structures has grown in popularity. These applications include composite risers and related SURF (subsea umbilicals, risers and flowlines) units. The composite industry has evolved in the development of advanced composites, such as thermoplastic composite pipes (TCP) and hybrid composite structures. However, there are gaps in the understanding of its performance in composite risers, hence the need for this review on the design, hydrodynamics and mechanics of composite risers. The review covers both the structure of the composite production riser (CPR) and its end-fittings for offshore marine applications. It also reviews the mechanical behaviour of composite risers, their microstructure and strength/stress profiles. In principle, designers now have a greater grasp of composite materials. It was concluded that composites differ from standard materials such as steel. Basically, composites have weight savings and a comparative stiffness-to-strength ratio, which are advantageous in marine composites. Also, the offshore sector has grown in response to newer innovations in composite structures such as composite risers, thereby providing new cost-effective techniques. This comprehensive review shows the necessity of optimising existing designs of composite risers. Conclusions drawn portray issues facing composite riser research. Recommendations were made to encourage composite riser developments, including elaboration of necessary standards and specifications. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.