Nanomaterials have gained tremendous research interest over the years due to their unique physical and chemical properties. Computational methods, such as Density Functional Theory (DFT) calculations, are excitingly helpful with the study of nanomaterials, since they provide information under atomic scale. In this thesis, computational study of growth, thermodynamics, and electronics properties of nanomaterials are discussed. Firstly, DFT calculations are performed to study the growth, synthesis, thermodynamics, and stability of borophene, a newly emerged two-dimensional (2D) boron material, in order to give guidance and explanations to experiments. Secondly, the nano-thermodynamics in the phase transition process from graphene to 2D diamond is introduced, to reveal the energy competition during phase transformation that experiments are hard to catch. Next, a diamond-cubic boron nitride heterostructure system is proposed, its enhanced doping abilities over pure diamond are thoroughly investigated by a simple model. Finally, the stability and superconductivities of 2D gallium are studied to provide a new computational method to search materials under confinement.