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The total mass of a galaxy cluster is one of its most fundamental properties.Together with the redshift, the mass links observation and theory, allowing usto use the cluster population to test models of structure formation and toconstrain cosmological parameters. Building on the rich heritage from X-raysurveys, new results from Sunyaev-Zeldovich and optical surveys have stimulateda resurgence of interest in cluster cosmology. These studies have generallyfound fewer clusters than predicted by the baseline Planck LCDM model,prompting a renewed effort on the part of the community to obtain a definitivemeasure of the true cluster mass scale. Here we review recent progress on thisfront. Our theoretical understanding continues to advance, with numericalsimulations being the cornerstone of this effort. On the observational side,new, sophisticated techniques are being deployed in individual massmeasurements and to account for selection biases in cluster surveys. Wesummarise the state of the art in cluster mass estimation methods and thesystematic uncertainties and biases inherent in each approach, which are nowwell identified and understood, and explore how current uncertainties propagateinto the cosmological parameter analysis. We discuss the prospects forimprovements to the measurement of the mass scale using upcomingmulti-wavelength data, and the future use of the cluster population as acosmological probe.

The galaxy cluster mass scale and its impact on cosmological constraints from the cluster population