Transpression and transtension are strike-slip deformations that deviate from simple shear because of a component of, respectively, shortening or extension orthogonal to the deformation zone. These three-dimensional non-coaxial strains develop principally in response to obliquely convergent or divergent relative motions across plate boundary and other crustal deformation zones at various scales. The basic constant-volume strain model with a vertical stretch can be modified to allow for volume change, lateral stretch, an oblique simple shear component, heterogeneous strain and steady-state transpression and transtension. The more sophisticated triclinic models may be more realistic but their mathematical complexity may limit their general application when interpreting geological examples. Most transpression zones generate flattening (k < 1) and transtension zones constrictional (k > 1) finite strains, although exceptions can occur in certain situations. Relative plate motion vectors, instantaneous strain (or stress) axes and finite strain axes are all oblique to one another in transpression and transtension zones. Kinematic partitioning of non-coaxial strike-slip and coaxial strains appears to be a characteristic feature of many such zones, especially where the far-field (plate) displacement direction is markedly oblique (<20 ~ to the plate or deformation zone boundary. Complex foliation, lineation and other structural patterns are also expected in such settings, resulting from switching or progressive rotation of finite strain axes. The variation in style and kinematic linkage of transpressional and transtensional structures at different crustal depths is poorly understood at present but may be of central importance to understanding the relationship between deformation in the lithospheric mantle and crust. Existing analyses of obliquely convergent and divergent zones highlight the importance of kinematic boundary conditions and imply that stress may be of secondary importance in controlling the dynamics of deformation in the crust and lithosphere.