During the past 150 years, a wide range of processes have been invoked to explain the mechanism by which magmas differentiate.These may be divided into those which operate essentially in the liquid state, such as liquid immiscibility and thermogravitational diffusion, and those which involve some form of crystal-liquid fractionation. It is now generally accepted that the latter are the most important. Many of the models developed during the past twenty years to explain magmatic differentiation have their roots in ideas first proposed in the early years of this century. This review presents some of the historical background to the subject and attempts to summarize some of the more recent developments. Alfred Harker's perceptive study of in-situ crystallization within a high-level intrusion (Carrock Fell in the English Lake District), published in volume 50 of the Quarterly Journal of the Geological Society in 1893, clearly laid the foundations for many modern theories. In 1900 he introduced the oxide-oxide variation diagram, which is still widely used to depict the geochemical variations within suites of cogenetic igneous rocks. Studies of phase equilibria in synthetic and natural systems by Bowen and his contemporaries, during the 1920s and 30s, provided the theoretical background needed to understand the complex processes involved in fractional crystallization of magmas. In the past decade mathematical modelling has allowed a more quantitative approach to the problem.