The ocean and human activities related to the sea are under increasing pressure due to climate change, widespread pollution, and growth of the offshore energy sector. Data, in under-sampled regions of the ocean and in the offshore patches where the industrial expansion is taking place, are fundamental to manage successfully a sustainable development and to mitigate climate change. Existing technology cannot cope with the vast and harsh environments that need monitoring and sampling the most. The limiting factors are, among others, the spatial scales of the physical domain, the high pressure, and the strong hydrodynamic perturbations, which require vehicles with a combination of persistent autonomy, augmented efficiency, extreme robustness, and advanced control. In light of the most recent developments in soft robotics technologies, we propose that the use of soft robots may aid in addressing the challenges posed by abyssal and wave-dominated environments. Nevertheless, soft robots also allow for fast and low-cost manufacturing, presenting a new potential problem: marine pollution from ubiquitous soft sampling devices. In this study, the technological and scientific gaps are widely discussed, as they represent the driving factors for the development of soft robotics. Offshore industry supports increasing energy demand and the employment of robots on marine assets is growing. Such expansion needs to be sustained by the knowledge of the oceanic environment, where large remote areas are yet to be explored and adequately sampled. We offer our perspective on the development of sustainable soft systems, indicating the characteristics of the existing soft robots that promote underwater maneuverability, locomotion, and sampling. This perspective encourages an interdisciplinary approach to the design of aquatic soft robots and invites a discussion about the industrial and oceanographic needs that call for their application.