Underwater stereo-video measurement systems are used widely for counting and measuring fish in aquaculture, fisheries and conservation management. To determine population counts, spatial or temporal frequencies, and age or weight distributions, snout to fork length measurements are captured from the video sequences, most commonly using a point and click process by a human operator. Current research aims to automate the measurement and counting task in order to improve the efficiency of the process and expand the use of stereo-video systems within marine science. A fully automated process will require the detection and identification of candidates for measurement, followed by the snout to fork length measurement, as well as the counting and tracking of fish. This paper presents a review of the techniques used for the detection, identification, measurement, counting and tracking of fish in underwater stereo-video image sequences, including consideration of the changing body shape. The review will analyse the most commonly used approaches, leading to an evaluation of the techniques most likely to be a general solution to the complete process of detection, identification, measurement, counting and tracking.