Acoustic underwater sensors, also termed hydrophones, are used by the Swedish Armed Forces to record acoustic signals in the underwater environment to, among other things, detect hostile activity. Analysing the acoustic signals that are thus collected requires significant manual work. This report examines possibilities to automate this process to some degree by applying methods from the area of artificial intelligence and deep learning. Assuming that the targets we want to be able to detect occur infrequently, and that they differ acoustically to some extent from the "normal" acoustic environment, we look especially at methods for anomaly detection. The report provides a survey over different methods for anomaly detection in the literature, analyses the practical considerations and challenges for their application, and identifies a set of promising method candidates. Finally, it sketches out a plan for how future research efforts may be structured to evaluate these methods and eventually bring them to practical use in the underwater environment.