The growth and properties of Si1-yCy and Si1-x-yGexCy alloys pseudomorphically strained on Si(001) will be critically reviewed. Although the bulk solubility of carbon in silicon is small, epitaxial layers with more than 1 at.% C can be fabricated by molecular beam epitaxy and different chemical vapour deposition techniques. One of the most crucial questions is the relation between substitutional and interstitial carbon incorporation, which has a large impact on the electrical and optical properties of these layers. We will show that the interstitial to substitutional carbon ratio is strongly influenced by the chosen growth conditions, like growth temperature and Si growth rate. In addition, angle-resolved X-ray photoelectron spectroscopy measurements indicate a surface segregation of interstitial carbon-containing complexes (more significant for higher growth temperature). Substitutionally incorporated C atoms allow strain manipulation, including the growth of an inversely strained Si1-x-yGexCy. layer. Local ordering effects due to atomic size differences and the growth on reconstructed surfaces, the mechanical and structural properties, and the influence of C atoms on band structure of Si and SiGe layers will be discussed.