We follow the history of nanobubbles from the earliest experiments pointing to their existence to recent years. We cover the effect of Laplace pressure on the thermodynamic stability of nanobubbles and why this implies that nanobubbles are thermodynamically never stable. Therefore, understanding bubble stability becomes a consideration of the rate of bubble dissolution, so the dominant approach to understanding this is discussed. Bulk nanobubbles (or fine bubbles) are treated separately from surface nanobubbles as this reflects their separate histories. For each class of nanobubbles, we look at the early evidence for their existence, methods for the production and characterization of nanobubbles, evidence that they are indeed gaseous, or otherwise, and theories for their stability. We also look at applications of both surface and bulk nanobubbles.