There is increasing demand, in particular from the medical field, for assays capable of detecting sub-pM macromolecular concentrations with high specificity. Methods for detecting single bio/macromolecules have already been developed based on a variety of transduction mechanisms, which represents the ultimate limit of mass sensitivity. Due to limitations imposed by mass transport and binding kinetics, however, achieving high concentration sensitivity additionally requires the massive parallelization of these single-molecule methods. This leads to a new sort of 'digital' assay based on large numbers of parallel, time-resolved measurements aimed at detecting, identifying and counting discrete macromolecular events instead of reading out an average response. In this Tutorial Review we first discuss the challenges inherent to trace-level detection and the motivations for developing digital assays. We then focus on the potential of recently developed single-entity impact electrochemistry methods for use in digital sensors. These have the inherent advantage of relying on purely electrical signals. They can thus in principle be implemented using integrated circuits to provide the parallelization, readout and analysis capabilities required for digital sensors.