Diffusionless transformations occur when atoms in a crystal move cooperatively and nearly simultaneously, distorting the crystal into a new shape. The martensite transformation is the most famous diffusionless transformation, owing to its importance in steel metallurgy. In a martensitic transformation the change in crystal structure occurs by shears and dilatations, and the atom displacements accommodate the shape of the new crystal. The atoms do not move with independent degrees of freedom, so the change in configurational entropy is negligible or small. The entropy of a martensitic transformation is primarily vibrational (sometimes with electronic entropy, or magnetic entropy for many iron alloys). This chapter begins with a review of dislocations, and how their glide motions can give crystallographic shear. Some macroscopic and microscopic features of martensite are then described, followed by a two-dimensional analog for a crystallographic theory that predicts the martensite “habit plane” (the orientation of a martensite plate in its parent crystal). Displacive phase transitions are explained more formally with Landau theories having anharmonic potentials and vibrational entropy. Phonons are discussed from the viewpoint of soft modes and instabilities of bcc structures that may be relevant to diffusionless transformations.