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Monitoring on the basis of sound recordings, or passive acoustic monitoring, can complement or serve as an alternative to real‐time visual or aural monitoring of marine mammals and other animals by human observers. Passive acoustic data can support the estimation of common, individual‐level ecological metrics, such as presence, detection‐weighted occupancy, abundance and density, population viability and structure, and behaviour. Passive acoustic data also can support estimation of some community‐level metrics, such as species richness and composition. The feasibility of estimation and certainty of estimates is highly context dependent, and understanding the factors that affect the reliability of measurements is useful for those considering whether to use passive acoustic data. Here, we review basic concepts and methods of passive acoustic sampling in marine systems that often are applicable to marine mammal research and conservation. Our ultimate aim is to facilitate collaboration among ecologists, bioacousticians, and data analysts. Ecological applications of passive acoustics require one to make decisions about sampling design, which in turn requires consideration of sound propagation, sampling of signals, and data storage. One also must make decisions about signal detection and classification and evaluation of the performance of algorithms for these tasks. Investment in the research and development of systems that automate detection and classification, including machine learning, are increasing. Passive acoustic monitoring is more reliable for detection of species presence than for estimation of other species‐level metrics. Use of passive acoustic monitoring to distinguish among individual animals remains difficult. However, information about detection probability, vocalisation or cue rate, and relations between vocalisations and the number and behaviour of animals increases the feasibility of estimating abundance or density. Most sensor deployments are fixed in space or are sporadic, making temporal turnover in species composition more tractable to estimate than spatial turnover. Collaborations between acousticians and ecologists are most likely to be successful and rewarding when all partners critically examine and share a fundamental understanding of the target variables, sampling process, and analytical methods. [ABSTRACT FROM AUTHOR]