Due to its exceptional electrical, mechanical, and chemical properties, SiC is currently receiving attention as an alternative to Si for use in micro- and nanoelectromechanical systems (MEMS and NEMS). This paper reviews several key achievements that have significantly advanced the development of SiC MEMS and NEMS. These include AP- and LPCVD processes for MEMS-suitable polycrystalline 3C-SiC, alternatives to reactive ion etching for multilayer poly-SiC surface micromachining, and fabrication techniques for single crystalline 3C-SiC nanomechanical resonators with fundamental resonant frequencies in the GHz range.