Here we review the characteristics of "van der Waals epitaxy" (vdWE) as an alternative epitaxy mechanism that has been demonstrated as a viable method for circumventing the lattice matching requirements for epitaxial growth. Particular focus is given on the application of vdWE for nonplanar nanostructures. We highlight our works on the vdWE growth of nanowire arrays, tripods, and tetrapods from various semiconductors (ZnO, ZnTe, CdS, CdSe, CdSxSe1-x, CdTe, and PbS) on muscovite mica substrates, irrespective of the ensuing lattice mismatch. We then address the controllability of the synthesis and the growth mechanism of ZnO nanowires from catalyst-free vdWE in vapor transport growth. As exemplified herein with optical characterizations of ZnO and CdSe nanowires, we show that samples from vdWE may possess properties that are as excellent as those from conventional epitaxy. With our works, we aim to advocate vdWE as a prospective universal growth strategy for nonplanar epitaxial nanostructures.