We discuss the strategies essential for the growth of high-quality (Al,Ga)N/GaN and (Ga,In)N/GaN heterostructures on SiC(0001) substrates by molecular beam epitaxy (MBE) using either N-2 plasma discharge or NH3 cracking as an active nitrogen source. Optimization of substrate preparation, nucleation, and growth conditions are the important issues to improve the surface morphology, interface abruptness, structural integrity, and electronic properties. A breakthrough in preparing the SiC(0001) surface was achieved by ex situ etching in H-2 at 1600 degrees C and subsequent in, situ cleaning via several cycles of Ga deposition and flash-off at 800 degrees C. By far the best results are then obtained, when growth is initiated directly, i.e., without any specific nucleation phase, for both plasma assisted (PA)MBE and reactive (R)MBE. Using growth rates of 0.5-1.2 mu m/h the optimum growth temperature T-s was found to be 700 degrees C for GaN. Any deviation from the optimum T-s and the optimum III/V flux ratio can be easily detected by reflection high energy electron diffraction and adjusted appropriately. Using these careful optimization strategies, both PAMBE and RMBE produce (Al,Ga,Ln)N heterostructures on SiC(0001) of high morphological, structural, and electronic quality in a very reproducible manner. The only difference between the two nitrogen sources is the very limited incorporation of In in (Ga,In)N in the presence of hydrogen from the NH3 cracking on the growing surface. In PAMBE-grown (Ga,In)/GaN single and multiple quantum wells we achieved In mole fractions from 0.05 to 0.70 in 3 nm wells which very efficiently emit in the violet to yellow spectral range at 300 K.