Spawned by fast paced progress in marine science and technology, the past two decades have witnessed growing interest in ocean exploration and exploitation for scientific and commercial purposes, the development of technological products for the maritime and offshore industries, and a host of other activities in which the marine environment takes center stage. In this context, marine robotics has steadily emerged as a key enabling technology for the execution of increasingly complex and challenging missions at sea. Intensive research and development in this field have led to major advances and shown unequivocally the effectiveness and reliability of marine robotics solutions in several domains. This progress goes hand in hand with the availability of increasingly sophisticated acoustic networks for multiple, cooperative missions involving surface and underwater robots. At the root of this trend is the fruitful dialogue between robotic systems developers and end-users with the capacity to convert general mission objectives into functional and technical specifications that serve as application-driven requirements for engineering development. The result is the tremendous progress observed in the consolidated methodologies and procedures adopted and the consequent impact on science, industry, and the society at large. In spite of the progress in the area, however many challenges must still be faced and novel applications will continue to set further requirements for future generations of marine robots and their enabling systems. The time is therefore appropriate to overview recent trends in the field of marine robotics and assess their impact on several important application domains. With these objectives in mind, in the present paper we highlight key technological achievements in the field, analyze some of the shortcomings encountered, and indicate specific issues that warrant further research and development effort. To this end, we review a number of highly representative projects in the field, with due account for the theoretical frameworks upon which technological developments build upon. Finally, the paper concludes with an outlook on the future of marine robotics, both from a theoretical and practical standpoint, and describes recently initiated projects that hold promise for the development of advanced tools and systems for ocean exploration and exploitation.