The classical theory of the crystallography of martensitic transformations developed in the 1950s is based on the notion that the interface between the parent and product phases is an invariant plane of the shape deformation. Underlying this hypothesis is the expectation that such interfaces do not exhibit long-range strain, and the geometric theory is an algorithm for finding invariant planes, the orientation relationship and transformation displacement. In the context of ferrous alloys, the classical theory has been applied successfully to transformations with {295} habit planes, but is less satisfactory for {575} for example. A new model of martensitic transformations has been presented recently based on dislocation theory, incorporating developments in the understanding of the topological properties of interfacial defects. Topological arguments show that glissile motion of transformation dislocations, or disconnections, can only occur in coherent interphase interfaces. Hence, the interface in the model comprises coherent terraces with a superimposed network of disconnections and crystal dislocations. It is demonstrated explicitly that this defect network accommodates the coherency strains, and that lateral motion of the disconnections across the interface effects transformation in a diffusionless manner. Moreover, it is shown that a broader range of habit planes is predicted on the basis of the semi-coherent interface model than the invariant plane notion. In the case of ferrous alloys, it will be shown that a range of viable solutions arise which include {575}.