Directional recrystallisation processing is a solid-state process in which a specimen traverses a sharp hot zone and one or a few grains grow as they pass through the hot zone. The mechanism can be either a primary recrystallisation or secondary recrystallisation process, or a combination of both. The mechanism can be either primary recrystallisation or secondary recrystallisation process, or a combination of both. Directional recrystallisation was invented more than 80 years ago to achieve columnar grain structures or single crystals that have enhanced mechanical properties. This review discusses the effects of both processing parameters, including the temperature gradient, hot-zone velocity, and annealing temperature, and microstructural parameters, including stored energy, grain size, initial texture, solutes, and both soluble and insoluble particles, on the resulting microstructures. The results of simulations of directional recrystallisation, including Monte Carlo simulations, Front-Tracking methods, and phase-field simulations, are also reviewed. Finally, the effects of directional recrystallisation on material properties are discussed.