Abstract van der Waals epitaxy (VDWE) is an ideal method for growing 2D materials and topological insulators (TIs) onto a variety of substrates for heterostructure and integrated circuit technologies. The characteristics of VDWE include rotational alignment with the substrate, strain-free growth, and no misfit dislocations despite significant lattice mismatch. Such properties are critical to enable devices which use the unique characteristics of transition metal dichalcogenides (TMDs) and TIs. These include defect tolerance, spin-polarized transport, reduced leakage currents, and tunable band gaps. In this review, the growth modes and advantages of VDWE are introduced along with a brief history of the field. Then the most important issues regarding the VDWE of TMDs and TIs in particular are discussed, including grain size control, defect density, doping, rotational alignment, and electronic transport. Finally, we provide an overview of the progress made in recent years along with an outlook to address the remaining issues facing VDWE and these materials.