With the continuous development of space and sensor technologies during the last 40 years, ocean remote sensing has entered into the big-data era with typical five-V (volume, variety, value, velocity and veracity) characteristics. Ocean remote-sensing data archives reach several tens of petabytes and massive satellite data are acquired worldwide daily. To precisely, efficiently and intelligently mine the useful information submerged in such ocean remote-sensing data sets is a big challenge. Deep learning—a powerful technology recently emerging in the machine-learning field—has demonstrated its more significant superiority over traditional physical- or statistical-based algorithms for image-information extraction in many industrial-field applications and starts to draw interest in ocean remote-sensing applications. In this review paper, we first systematically reviewed two deep-learning frameworks that carry out ocean remote-sensing-image classifications and then presented eight typical applications in ocean internal-wave/eddy/oil-spill/coastal-inundation/sea-ice/green-algae/ship/coral-reef mapping from different types of ocean remote-sensing imagery to show how effective these deep-learning frameworks are. Researchers can also readily modify these existing frameworks for information mining of other kinds of remote-sensing imagery.