One of the frontiers in the field of biosensors is the ability to quantify specific target molecules with enough precision to count individual units in a test sample, and to observe the characteristics of individual biomolecular interactions. Technologies that enable observation of molecules with "digital precision" have applications for in vitro diagnostics with ultra-sensitive limits of detection, characterization of biomolecular binding kinetics with a greater degree of precision, and gaining deeper insights into biological processes through quantification of molecules in complex specimens that would otherwise be unobservable. In this review, we seek to capture the current state-of-the-art in the field of digital resolution biosensing. We describe the capabilities of commercially available technology platforms, as well as capabilities that have been described in published literature. We highlight approaches that utilize enzymatic amplification, nanoparticle tags, chemical tags, as well as label-free biosensing methods.