Since the first isolation of graphene from graphite in 2004, atomically thin or layered materials have been occupying the central stage of today's condensed matter physics and materials sciences because of their rich and exotic properties in two dimensions (2D). Many members of the ever-expanding 2D materials family, such as graphene, silicene, phosphorene, borophene, hexagonal boron nitride, transition metal dichalcogenides, and even the strong topological insulators, share the distinct commonality of possessing relatively weak van der Waals (vdW) interlayer coupling, whereas each member may invoke its own fabrication approaches, and is characterized by its unique properties. In this review article, we first discuss the major atomistic processes and related morphological evolution in the epitaxial growth of vdW layered materials, including nucleation, diffusion, feedstock dissociation, and grain boundaries. Representative systems covered include the vdW epitaxy of both monolayered 2D systems and their lateral or vdW-stacked heterostructures, emphasizing the vital importance of the vdW interactions in these systems. We also briefly highlight on some of the recent advances in the property optimization and functionalization of the 2D materials, especially in the fields of optics, electronics, and spintronics. /compmolsci 6 7 8 FIGURE 1 | Binding energies of C-C dimers on flat metal (111) surfaces with respect to the C-C distance (a) and the preference of C-C dimer formation on close-packed transition metal surfaces (b). The inset in (a) shows the top view of a C-C dimer on a closepacked metal surface. (Reprinted with permission from Ref 42.FIGURE 4 | Minimum energy paths of C diffusion within and between the different regions on (a) Cu(111) and (b) Ni (111). Here, Sub(1) and Sub(2) represent the first and second subsurface sites, respectively. The numbers in the horizontal axes correspond to the routes shown in the inset of (a). (