Persistence length is the foremost measure of DNA flexibility. Its origins lie in polymer theory which was adapted for DNA following the determination of B-DNA structure in 1953. There is no single definition of persistence length used, and the links between published definitions are based on assumptions which may, or may not be, clearly stated. DNA flexibility is affected by local ionic strength, solvent environment, bound ligands and intrinsic sequence-dependent flexibility. This article is a review of persistence length providing a mathematical treatment of the relationships between four definitions of persistence length, including: correlation, Kuhn length, bending, and curvature. Persistence length has been measured using various microscopy, force extension and solution methods such as linear dichroism and transient electric birefringence. For each experimental method a model of DNA is required to interpret the data. The importance of understanding the underlying models, along with the assumptions required by each definition to determine a value of persistence length, is highlighted for linear dichroism data, where it transpires that no model is currently available for long DNA or medium to high shear rate experiments.