  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 us
to use the cluster population to test models of structure formation and to
constrain cosmological parameters. Building on the rich heritage from X-ray
surveys, new results from Sunyaev-Zeldovich and optical surveys have stimulated
a resurgence of interest in cluster cosmology. These studies have generally
found fewer clusters than predicted by the baseline Planck LCDM model,
prompting a renewed effort on the part of the community to obtain a definitive
measure of the true cluster mass scale. Here we review recent progress on this
front. Our theoretical understanding continues to advance, with numerical
simulations being the cornerstone of this effort. On the observational side,
new, sophisticated techniques are being deployed in individual mass
measurements and to account for selection biases in cluster surveys. We
summarise the state of the art in cluster mass estimation methods and the
systematic uncertainties and biases inherent in each approach, which are now
well identified and understood, and explore how current uncertainties propagate
into the cosmological parameter analysis. We discuss the prospects for
improvements to the measurement of the mass scale using upcoming
multi-wavelength data, and the future use of the cluster population as a
cosmological probe.
