In the post-Graphene era, there has been a significant upsurge of interest on materials thinned down to its one or few atomic / molecular layer limit, and then exploring the new physics and applications emanating from these two-dimensional (2D) or quasi-2D nanostructures. Apart from Graphene and its analogues, there have been attempts to form 2D alloy nanosheets exhibiting tunable band gap. The other emerging class of 2D material that is being explored exhaustively is the layered transition metal dichalcogenide family viz. MX2 (M=TM, X=S, Se, Te). For example, there is an interesting manifestation of quantum size effect on the electronic behavior of layered VX2 as a function of the number of layers. Many of these quasi-2D TMDC’s, grown epitaxially on metallic or semiconducting substrates, result in lattice matched / mismatched heterostructures with different kinds of bonding ranging from weak Van der Waals bonding to relatively stronger ionic/covalent bonding. Physical and chemical properties of such overlayers often get modulated by the sub-surface layers of the corresponding substrates, leading to manifestation of new properties. In this talk, I shall discuss how density functional theory (DFT) based first principles simulation can be used in designing different classes of 2D materials and also to functionalize these for various applications in materials science and device physics. Finally, I shall highlight the increasing relevance of combining machine learning and combinatorial techniques with DFT data base on 2D and quasi-2D materials.