Many marine animals use sound passively or actively for communication, foraging, predator avoidance, navigation, and to sense their environment. The advent of acoustic recording tags has allowed biologists to get the on-animal perspective of the sonic environment and, in combination with movement sensors, to relate sounds to the activities of the tagged animal. These powerful tools have led to a wide range of insights into the behaviour of marine animals and have opened new opportunities for studying the ways they interact with their environment. Acoustic tags demand new analysis methods and careful experimental design to optimize the consistency between research objectives and the realistic performance of the tags. Technical details to consider are the suitability of the tag attachment to a given species, the accuracy of the tag sensors, and the recording and attachment duration of the tag. Here we consider the achievements, potential, and limitations of acoustic recording tags in studying the behaviour, habitat use and sensory ecology of marine mammals, the taxon to which this technology has been most often applied. We examine the application of acoustic tags to studies of vocal behaviour, foraging ecology, acoustic tracking, and the effects of noise to assess both the breadth of applications and the specific issues that arise in each.