The ability to break up a volume of fluid into smaller pieces that are confined or separated to prevent molecular communication/transport is a key capability intrinsic to microfluidic systems. This capability has been used to develop or implement digital versions of traditional molecular analysis assays, including digital PCR and digital immunoassays/ELISA. In these digital versions, the concentration of the target analyte is in a range such that, when sampled into smaller fluid volumes, either a single molecule or no molecule may be present. Subsequent amplification is sensitive enough to obtain a digital readout of the presence of these target molecules. Advantages of such approaches that are claimed include quantification without calibration and robustness to variations in reaction conditions or times because the digital readout is less sensitive to absolute signal intensity levels. Weaknesses of digital approaches include a lower dynamic range of concentrations over which the assay is sensitive, which depends on the total volume that can be analyzed. We highlight recent efforts to expand the dynamic range of digital assays based on exploiting reaction/diffusion phenomena. A side-by-side study that evaluates the strengths of digital assays reveals that the majority of these claims are supported, with specific caveats. Finally, we highlight approaches to apply digital assays to analyze new types of reactions, including the active transport of protons across membranes by ATPases at the single protein level - perhaps opening up new biophysical understanding and screening opportunities, similar to widely deployed single-molecule ion channel analysis.