Since the discovery of graphene, two-dimensional materials have been the focus of interest in various branches in scientific community. Wide range of ultra-thin materials have been investigated both theoretically and experimentally such as metal chalcogenides, Xenes and h-BN. In addition to this, two-dimensional (2D) van der Waals heterojunctions have become one of the central research topics due to their wide range of possibilities. Since 2D van der Waals heterostructures are combinations of two or more ultra-thin materials with different properties, creating a heterostructure with desired optical, electrical and/or mechanical property is theoretically probable. Motivated by these, this thesis focus on the investigation of structural, vibrational and electronic properties of 2D materials and their heterostructures by means of density functional theory-based first-principle calculations. In chapter 3, single-layer Ge3N4 is shown to be both electronically and dynamically stable. Also, simulated Raman spectrum of single-layer Ge3N4 have characteristic vibrational properties. Another property of single-layer Ge3N4 is that it is a indirect band gap semiconductor and this property is uneffected by external strain. And lastly, the value of band gap varies with the applied external strain. In chapter 4, a dynamically stable single layer structure of AlAs is proposed and four possible stackings of AlAs/InSe heterobilayer were investigated. Electronic band dispersions revealed that all four stackings are direct band gap semiconductors and have type-II alignment. Moreover, simumlated raman spectra revelaed that identification of the 1T and 2H phase can be done with Raman spectroscopy. The band gap can be tuned based on the direction and magnitude of the electric field. Direct to indirect band gap transition as well as heterojunction type changes from type II to type I occurs under negative electric field.