Advanced transmission electron microscopy techniques have been used to study strain formation in low dimensional structures grown by molecular beam epitaxy (MBE) and after Ge(+)- or Si(+)-ion implantation and subsequent annealing. Convergent beam electron diffraction patterns (CBED) show that the lattice parameter a of defect-free 3C-SiC MBE quantum films corresponds to that of cubic bulk SiC, however the structure is rhombohedral distorted. A highly defective 3C-SiC: layer is formed after room temperature implantation of Ge(+) and annealing, Cracks in the cubic layer have wide strain fields which result in a 6H --> 3C polytype transformation. In contrast to the thin cubic layers grown by MBE, the resulting cubic stripes are not distorted. ALCHEMI (atom location by channelling enhanced microanalysis) experiments in combination with Bloch wave calculations suggested that for certain implantation conditions the Ge atoms are clustered and located on interstitial positions, straining the SiC matrix. Si nanocrystals formed in the 6H-SiC matrix by Si implantation are unstrained although stacking faults (SFs) parallel to (0001) planes are seen. For Si nanocrystals sown on the surface of cubic SiC, SFs are often seen propagating from the 3C-SiC layer to the dot. Crystals that are 5 to 15nm in size grow in two orientations differing in the misfit to the substrate showing in both orientations only a little strain however larger crystals grow only with the orientation relationship of (111)(SiC) // (111)(Si) and (112)(SiC) // (112)(Si).