Since the 1990s, developments in room-temperature single-molecule spectroscopy, imaging, and manipulation have allowed studies of single-molecule behaviors in vitro and in living cells. Unlike conventional ensemble studies, single-molecule enzymology is characterized by ubiquitous fluctuations of molecular properties. The understanding of such single-molecule stochasticity is pertinent to many life processes. Applications of single-molecule technologies to biology and medicine have become a major force in life sciences. DNA exists as single molecules in an individual cell. Consequently, gene expression is stochastic. Single-molecule gene expression experiments in live single cells have allowed quantitative description and mechanistic interpretations. The fact that there are 46 different individual DNA molecules (chromosomes) in a human cell dictates that genomic variations occur stochastically and cannot be synchronized among individual cells. Probing such genomic variations requires single-cell and single-molecule measurements, which have recently been made possible, opening opportunities to investigate and diagnose cancer, and to avoid genetic disorders in newborns.