After nearly 20 years of data-taking, the measurements made with the Pierre Auger Observatory represent the largest collection of ultra-high-energy cosmic ray (UHECR) data so far assembled from a single instrument. Exploring this data set led to a deeper understanding of the UHECR flux and many surprises. In particular, studies aiming to investigate and leverage the mass composition of UHECRs have played an important role in empowering discovery. This contribution will present an overview of the analyses of primary mass composition carried out during the first phase of the Observatory. The overview includes analyses derived from measurements made by the surface, fluorescence, and radio detectors covering energies ranging from 0.1 EeV up to 100 EeV. Special attention will be given to recent advances and results to provide a complete picture of UHECR mass composition at the Observatory as it moves to its next phase, AugerPrime. Additionally, specific updates will be given to studies focusing on mass trends from surface detector rise-times, $𝑋_{\rm max}{}$dependent anisotropies, and UHECR beam characterization using the correlation between $𝑋_{\rm max}{}$and signal amplitudes at the ground.