Multiple populations in massive star clusters under the magnifying glass
  of photometry: Theory and tools
  The existence of star-to-star light-element abundance variations in massive
Galactic and extragalactic star clusters has fairly recently superseded the
traditional paradigm of individual clusters hosting stars with the same age,
and uniform chemical composition. Several scenarios have been put forward to
explain the origin of this multiple stellar population phenomenon, but so far
all have failed to reproduce the whole range of key observations.
  Complementary to high-resolution spectroscopy, which has first revealed and
characterized chemically the presence of multiple populations in Galactic
globular clusters, photometry has been instrumental in investigating this
phenomenon in much larger samples of stars --adding a number of crucial
observational constraints and correlations with global cluster properties-- and
in the discovery and characterization of multiple populations also in
Magellanic Clouds' intermediate age clusters.
  The purpose of this review is to present the theoretical underpinning and
application of the photometric techniques devised to identify and study
multiple populations in resolved star clusters. These methods have played and
continue to play a crucial role in advancing our knowledge of the cluster
multiple population phenomenon, and promise to extend the scope of these
investigations to resolved clusters even beyond the Local Group, with the
launch of the James Webb Space Telescope.
