Recent progress in SiC homoepitaxial growth at the authors' roup is reviewed. The background doping and deep trap concentrations have been reduced to 2 x 10(13) cm(-3) and 4 x 10(10) cm(-3), respectively, for 4H-SiC(0001) epilayers; grown by horizontal hot-wall CVD. High-temperature growth by chimney-type vertical hot-wall CVD has resulted in a high growth rate of 25 mum/h and a low doping concentration of 1 x 10(13) cm(-3) or less. A novel crystal orientation, 4H-SiC(03 (3) over bar8), is proposed as an attractive alternative, and is compared with off-axis (0001) and (11 (2) over bar0) from viewpoints of crystal growth and impurity doping. Remaining issues in SiC epitaxy are discussed.