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Motivated by the exciting properties of metal halide perovskites in photovoltaic applications, there is an evolving need to further explore the limitations of this class of materials in broader fields and high end optoelectronics, which requires better control over the film structure, defect levels, and quality. Epitaxial growth has been ubiquitously deployed in the semiconducting industry. This affords routes to precisely align the atomic arrangement to control the structure and strain and achieve the highest levels of optoelectronic performance. In this review, the recent emergence and progress in the epitaxial growth of metal halide perovskites are introduced within the context of epitaxial and quasiepitaxial approaches, and recent advances are surveyed from growth methods to application integration. The main criteria distinguishing epitaxy and quasiepitaxy, i.e., lattice matching and ordering, can be deployed to direct the selection of proper substrates, growth methods, and precursors for various applications.