Abstract: Two dimensional (2D) materials have been a hot research area since the novel and easy fabrication method called “micro-mechanical cleavage” was introduced by Novoselov and Geim. After the success of graphene, several stable 2D and quasi-2D materials, such as BN, transition-metal dichalcogenides (TMD), and a few other layered complex oxides, with high crystal quality have also been obtained under ambient pressure. To enhance their applications, it is of critical importance to explore the tunability of their band gaps. We will present some of our recent ab initio studies on opening an electronic band gap in graphene based materials by doping small BN domains, formation of C-BN super-lattices, and adsorption of aromatic moleculars. For quasi-2D TMDs (such as MoS2), mechanical strains are promising alternatives, we have also investigate the physics and application of engineering bandgaps of TMDs. Recently, we start to explore the possibility of 2D materials in the more ionic regions.