Boron nitride has attracted a great deal of attention as a two dimensional (2D) insulator for substrate and gate dielectric applications in 2D electronics. Development of a scalable technique to grow mono- to few-layer h-BN on microelectronics compatible substrates is desirable. Work on the growth of atomically smooth BN and graphene on sapphire and Si is presented in this paper. Two approaches are described: i) growth of h-BN and graphene on Si and sapphire substrates using a catalyzing Cu thin film, and ii) low pressure metal organic chemical vapor deposition (MOCVD) growth on sapphire. In approach i) we discuss problems associated with the thermal instability of Cu at the interface with the substrate and show how the stability may be improved through the use of a thin Ni buffer layer or careful substrate selection. The correlation between Cu film morphology and h-BN (and graphene) quality is shown. In approach ii) we find two different growth modes, 3D island growth at low V/III ratios and self-terminating growth at high V/III ratios. Under self-terminating growth atomically smooth few-layer h-BN films are produced. Nitridation of the sapphire surface is found to promote this self-terminating growth by improving nucleation of BN on the substrate. Finally, we present results from the growth of graphene/h-BN on sapphire in a single process.