The different aspects of molecular beam epitaxy (MBE) for producing two-dimensional (Quantum well), one-dimensional (Quantum wire and rod), and zero-dimensional (Quantum dot) structures based on SiC for functional applications are discussed. Development and implementation of a suitable MBE growth procedure for fabrication of heteropolytypic layer sequences are demonstrated in context with thermodynamic considerations. Furthermore, the growth of onedimensional structures based on cubic wires and nanorod arrays, also grown on Si(111), is shown. Moreover, the perspectives of quantum dot structures and a novel way to form 3C-SiC-dot structures within alpha-SiC has been discussed.