The exceptional physical properties of two-dimensional (2D) van der Waals (vdW) materials have been extensively researched, driving advances in material synthesis. Epitaxial growth, a prominent synthesis strategy, enables the production of large-area, high-quality 2D films compatible with advanced integrated circuits. Typical 2D single crystals, such as graphene, transition metal dichalcogenides and hexagonal boron nitride, have been epitaxially grown at a wafer scale. A systematic summary is required to offer strategic guidance for the epitaxy of emerging 2D materials. Here we focus on the epitaxy methodologies for 2D vdW materials in two directions: the growth of in-plane single-crystal monolayers and the fabrication of out-of-plane homostructures. We first discuss nucleation control of a single domain and orientation control over multiple domains to achieve large-scale single-crystal monolayers. We analyse the defect levels and measures of crystalline quality of typical 2D vdW materials with various epitaxial growth techniques. We then outline technical routes for the growth of homogeneous multilayers and twisted homostructures. We further summarize the current strategies to guide future efforts in optimizing on-demand fabrication of 2D vdW materials, as well as subsequent device manufacturing for their industrial applications.
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