The main purpose of this work is to describe the surface growth phenomena. Initially, we give a brief introduction to the analytical studies, in particular, done by di erential equations such as Edward-Wilkinson and Kardar-Parisi-Zhang equations, and then introduce the discrete surface growth models as a means to describe these phenomena with a restricted number of rules. The universality properties of these models help us categorize them in three di erent classes, namely Gaussian, Edward-Wilkinson, and Kardar-Parisi-Zhang universality classes. Five di erent numerical growth models are explained, and the statistical properties of the growing interfaces in 1D systems are examined via computational studies. Growth properties of 1D structures are viewed in two di erent ways, one being the scaling exponent of roughness changing with respect to time, and the other the distribution of height uctuations. In this research, we show that our numerical simulation findings are in accord with the theoretical and analytical predictions. In addition, for the ballistic deposition and restricted solid-on-solid models, we introduce a binning method [1] which improves our numerical results. Moreover, we propose a novel modification on the ballistic deposition model by detecting the thin-deep wells on the interface and average them out which enables us to report an improvement in our numerical results with a noteworthy development on physical properties of the system. Furthermore, we investigate the e ect of the change of the deposition rate on the universal behavior of the system, as a result, we introduce critical values for the deposition rate with respect to the size of the system. With these modifications, we are one step closer to defining the complex behavior of the growth phenomena.