Based on the available literature, this article describes the advances made in cell culture of wheat. The importance of the age and physiological stage of the explant is discussed. The influence of the genotype is observed. The role of the components of the induction medium and in particular the role of auxin and kinetin, is investigated. The development of off-white callus and long-term culture of this callus facilitates the establishment of suspension culture - a source of totipotent protoplasts. This paper also focuses on the techniques which are used to introduce genes into wheat plants and on the somaclonal variation that occurs in a population of plants regenerated after tissue culture.