The cosmic evolution of galaxies' neutral atomic gas content is a major science driver for the Square Kilometre Array (SKA), as well as for its South African (MeerKAT) and Australian (ASKAP) precursors. Among the HI large survey programs (LSPs) planned for ASKAP and MeerKAT, the deepest and narrowest tier of the "wedding cake" will be defined by the combined L-band+UHF-band Looking At the Distant Universe with the MeerKAT Array (LADUMA) survey, which will probe HI in emission within a single "cosmic vuvuzela" that extends to z = 1.4, when the universe was only a third of its present age. Through a combination of individual and stacked detections (the latter relying on extensive multi-wavelength studies of the survey's target field), LADUMA will study the redshift evolution of the baryonic Tully--Fisher relation and the cosmic HI density, the variation of the HI mass function with redshift and environment, and the connection between HI content and galaxies' stellar properties (mass, age, etc.). The survey will also build a sample of OH megamaser detections that can be used to trace the cosmic merger history. This proceedings contribution provides a brief introduction to the survey, its scientific aims, and its technical implementation, deferring a more complete discussion for a future article after the implications of a recent review of MeerKAT LSP project plans are fully
worked out.