An account is given of the categorical duality which exists between bounded distributive lattices and compact totally order disconnected spaces. During the past decade, a wide range of structural problems concerning distributive lattices have been solved by the topological and order theoretic techniques provided by duality, and a representative selection of these is presented. In addition, certain related dualities are briefly considered, as are compact totally order disconnected spaces in their own right. The paper ends with a 'dictionary' of mutually dual properties.