In this talk, we will discuss current challenges and summarize our latest progresses in the growth of thick GaN layers on Si substrates and physics of the carbon impurity in GaN. We firstly propose a large lattice-mismatch induced stress control technology to grow crack-free GaN and high mobility AlGaN/GaN as well as InAl(Ga)N/GaN heterostructures on Si substrates. Then, a Ga vacancy engineering is demonstrated for growth of thick GaN layers on Si substrates and fabrication of quasi-vertical GaN devices. Finally, the C doping behaviors in GaN are discussed, including the observation of two localized vibrational modes of CN in GaN and clarifying the formation and dissociation process of C-H complex in GaN.