Recent developments in the field of molecular beam epitaxy (MBE) have rekindled interest in the subject of pseudomorphism: the stabilization of metastable phases by epitaxy. These developments have led to the growth of metastable films of α‐Sn, α‐Sn:Ge alloys, and BaxCa1−xF2solid solutions. Unlike the early examples of pseudomorphism, these films are relatively thick, i.e., ≳0.5 μm. This has permitted the first quantitative study of strain anisotropy in pseudomorphic films by the technique of double‐crystal x‐ray diffraction. The growth and investigation of such films using MBE techniques is a new and fertile area of materials research driven by the potentially useful properties which the films exhibit. In contrast with the relative ease with which α‐Sn, α‐Sn:Ge, and fluoride solid solutions can be grown by MBE, attempts to prepare metastable InSb1−xBixsolid solutions have encountered major problems due to the surface segregation of competing liquid eutectic phases on the growth surface. These developments are reviewed and future directions of research in the field of pseudomorphic growth by MBE are discussed.