Technologies for the growth of 3C-SiC with crystalline quality and crystal size similar to hexagonal counterparts (6H-or 4H-SiC) are still at the laboratory stage. There are several challenges in the control of polytype stability and formation of structural defects which have to be eliminated to reveal the full potential of this material. Nevertheless, 3C-SiC has been explored for various energy, environment and biomedical applications which significantly benefit from the intrinsic semiconductor properties of this material. The future of 3C-SiC and its applications depends on the advances which will be made in improving crystalline quality, enlarging crystal size and controlling doping levels which have not been entirely explored due to the lack of high quality 3C-SiC substrates. This paper reviews recent progress in growth and doping of thick 3C-SiC layers on hexagonal SiC substrates using sublimation epitaxy. It covers the growth process on off-axis substrates and defects occurrence, as well as the issue of obtaining high resistivity material.