Viable and general techniques that allow effective size control of triangular-shaped, single-crystal, monolayer h-BN domains grown by the CVD method, direct optical visualization of h-BN domains, and the cleaning of the h-BN surface to achieve reliable graphene device quality are reported for the first time. This study points to a critical role of the interfacial properties between the graphene and the monolayer h-BN in determining reliable, enhanced graphene-device performance.