Lamellar structures, having strong in-plane and weak (van der Waals) out-ofplane bonding, exhibit extraordinary properties when thinned down to their monolayer limit. Following the isolation of single layer graphene in 2004, there has been a rapid increase in the number of studies focusing on other novel two dimensional (2D) materials such as hexagonal Boron Nitride (BN), transition metal dichalcogenides (TMDs), post transition metal chalcogenides (PTMCs), silicene and black-phosphorus. Doping of 2D and bulk crystals is a well-known strategy that may lead to novel functionalities and significantly alters materials’ electronic, optical, and magnetic properties. In this regard, understanding of diffusion characteristic of dopant in a crystal via computational simulation is vital to enlighten physical insights of the experiment. In addition, investigation of degradation mechanisms of crystals at atomic-level is also still open question. In this sense, the density functional theory (DFT) is one of the most powerful and commonly used methods for such theoretical investigations. Moreover, measuring vibrational spectra of a material via Raman spectroscopy is powerful method to understand atomic vibrations that give information about physical properties of a material. In this regards, we investigate diffusion characteristics and degradation mechanism of several crystal (such as, perovskites and MoS2) by means of first-principles calculations based on density functional theory (DFT). In addition, Raman measurements are also carried out to investigate vibrational properties of the crystals. It is shown that few-layer MoS2 can be used for selective nitrogenation of graphene. In addition, red shift in photoluminescence peak of water interacted CsPbBr3 nanowires arise from detachment of surface ligand from surface of nanowire by presense of water molecules. Lastly, time-dependent photoluminescence measurement of Mn-doped CsPbCl3 shows that change in emission color under UV illumination is due to segregation of Mn atoms towards crystal surface. This thesis provides some important results for deeper understanding of degradation and diffusion mechanisms of dopants in 2D materials and perovskites.