This article describes the initial discovery and development of new approaches to SiC homoepitaxial and heteroepitaxial growth. These approaches are based upon the previously unanticipated ability to effectively supress two-dimensional nucleation of 3C-SiC on large basal plane terraces that form between growth steps when epitaxy is carried out on 4H-and 6H-SiC nearly on-axis substrates. After subdividing the growth surface into mesa regions, pure stepflow homoeptixay with no terrace nucleation was then used to grow all existing surface steps off the edges of screw-dislocation-free mesas, leaving behind perfectly on-axis (0001) basal plane mesa surfaces completely free of atomic-scale steps.Step-free mesa surfaces as large as 0.4 mm x 0.4 mm were experimentally realized, with the yield and size of step-free mesas being initally limited by substrate screw dislocations. Continued epitaxial growth following step-free surface formation leads to the formation of thin lateral cantilevers that extend the step-free surface area from the top edge of the mesa sidewalls. By selecting a proper pre-growth mesa shape and crystallographic orientation, the rate of cantilever growth can be greatly enhanced in a web growth process that has been used to (1) enlarge step-free surface areas and (2) overgrow and laterally relocate micropipes and screw dislocations. A new growth process, named step-free surface heteroepitaxy, has been developed to achieve 3C-SiC films on 4H-and 6H-SiC substrate mesas completely free of double positioning boundary and stacking fault defects. The process is based upon the controlled terrace nucleation and lateral expansion of a single island of 3C-SiC across a step-free mesa surface. Experimental results indicate that substrateepilayer lattice mismatch is at least partially relieved parallel to the interface without dislocations that undesirably thread through the thickness of the epilayer. These results should enable realization of improved SiC homojunction and heterojunction devices. In addition, these experiments offer important insights into the nature of polytypism during SiC crystal growth.