Ocean gliders are quiet, buoyancy-driven, long-endurance, profiling autonomous platforms. Gliders therefore possess unique advantages as platforms for Passive Acoustic Monitoring (PAM) of the marine environment. In this paper, we review available glider platforms and passive acoustic monitoring systems, and explore current and potential uses of passive acoustic monitoring-equipped gliders for the study of physical oceanography, biology, ecology and for regulatory purposes. We evaluate limiting factors for passive acoustic monitoring glider surveys, such as platform-generated and flow noise, weight, size and energy constraints, profiling ability and slow movement. Based on data from 34 passive acoustic monitoring glider missions, it was found that <13% of the time spent at sea was unsuitable for passive acoustic monitoring measurements, either because of surface communications or glider manoeuvre, leaving the remainder available for subsequent analysis. To facilitate the broader use of passive acoustic monitoring gliders, we document best practices and include workarounds for the typical challenges of a passive acoustic monitoring glider mission. Three research priorities are also identified to improve future passive acoustic monitoring glider observations: 1) Technological developments to improve sensor integration and preserve glider endurance; 2) improved sampling methods and statistical analysis techniques to perform population density estimation from passive acoustic monitoring glider observations; and 3) calibration of the passive acoustic monitoring glider to record absolute noise levels, for anthropogenic noise monitoring. It is hoped this methodological review will assist glider users to broaden the observational capability of their instruments, and help researchers in related fields to deploy passive acoustic monitoring gliders in their studies.