This thesis presents a variety of new two dimensional honeycomb-like structures and heterostructures; the main objective being to determine their fundamental electronic, magnetic, mechanical and optical properties for new device and material design. Utilization of existing two dimensional materials for nanoscale device design, understanding the fundamental properties of their composite structures, explaining the existing data on known two dimensional materials and using computational simulations to discover new materials are the main concerns of this thesis. We begin by assessing the validity of density functional theory on monolayer composites of graphene and boron nitride. We show that it is possible to grow vertical graphene / boron nitride heterostructures on top of each other and reveal the growth mechanisms at the atomistic level. We then utilize this vertical heterostructure for a nanoscale capacitor design by applying an external electric eld. We test and show how rst principles methods can be used to investigate the properties of materials under electric eld. After explaining the reliable methods, capacitance values are calculated for the model for various thicknesses, which show quantum mechanical size e ects at small separations that recede as the separations get larger; as the later is con rmed by experimental observations. The next part of the thesis, investigates the electronic properties of lateral graphene / boron nitride heterostructures, and show how these composites act di erently depending on the concentrations of graphene and boron nitride in the composite system. Namely, di erent behaviors of alloys, -doping and line compounds are revealed. Following this, these lateral heterostructures are utilized as nanoscale planar capacitors for atomically thin circuitry. As a nal remark on carbon and boron nitride nanocomposites, the next chapter of this thesis describes the growth mechanisms of one dimensional carbon/ boron nitride short atomic chains and show their stabilities at elevated temperatures. The electronic and magnetic properties of these chains exhibit even/odd disparity depending on the number of atoms in the chain. These chains also construct another two dimensional allotrope of graphene, namely graphyne, when connected to each other on the same plane. The properties of graphyne and its boron nitride analogue described in the following chapter introduces a new monolayer allotrope of carbon and boron nitride. The following chapter turns to silicon and germanium analogue of graphene, silicene and germanene. Dumbbell type reconstructions of silicene and germanene are introduced, which lead to layered silicene and germanene. Dumbbell units introduced here form the fundamental building blocks of experimentally observed layered silicene and germanene. The last chapter of the thesis looks at new material design and prediction studies based on computational simulations. Oxygenated silicene leads to a new monolayer piezoelectric material called silicatene. Finally, the monolayer structures of Group V elements nitrogen and antimony are also shown to be stable by phonon calculations and high temperature molecular dynamics simulations.