van der Waals (vdW) heteroepitaxy of semiconductors enables the integration of the semiconductor electronic and optoelectronic devices on virtually arbitrary substrates. In this chapter, we provide a review on recent progresses in the vdW epitaxy of semiconductor nanowires on two-dimensional atomic-layered materials (2d-ALMs). The efforts and challenges in various approaches for vdW epitaxy of semiconductor nanowires are reviewed. We pay particular attention in complementary studies on microscopically observed and theoretically simulated vdW epitaxial heterointerfaces. The methods of controlling the nucleation-growth processes for site-selective vdW epitaxy are discussed, followed by a brief review on optoelectronic device applications. The new opportunities and strategies for the vdW heteroepitaxial integration of semiconductors on 2d-ALMs are further discussed toward emerging functional electronics and optoelectronics.