A digital assay is one in which the sample is partitioned into many small containers such that each partition contains a discrete number of biological entities (0, 1, 2, 3, …). A powerful technique in the biologist’s toolkit, digital assays bring a new level of precision in quantifying nucleic acids, measuring proteins and their enzymatic activity, and probing single-cell genotypes and phenotypes. Part I of this review begins with the benefits and Poisson statistics of partitioning, including sources of error. The remainder focuses on digital PCR (dPCR) for quantification of nucleic acids. We discuss five commercial instruments that partition samples into physically isolated chambers (cdPCR) or droplet emulsions (ddPCR). We compare the strengths of dPCR (absolute quantitation, precision, and ability to detect rare or mutant targets) with those of its predecessor, quantitative real-time PCR (dynamic range, larger sample volumes, and throughput). Lastly, we describe several promising applications of dPCR, including copy number variation, quantitation of circulating tumor DNA and viral load, RNA/miRNA quantitation with reverse transcription dPCR, and library preparation for next-generation sequencing. This review is intended to give a broad perspective to scientists interested in adopting digital assays into their workflows. Part II focuses on digital protein and cell assays.