This paper presents an overview of studies dedicated to the atomic-discrete modeling of the growth process of film coatings that comprise mononitrides of transition and post-transition metals. The main modeling approaches are the Monte Carlo and molecular dynamics methods as well as their combinations with analytical contributions. The molecular dynamics method is more accurate compared to the Monte Carlo method but has disadvantages related to the time scale. Given this, the adoption of accelerated molecular dynamics methods is viewed as a promising approach for directly simulating the specified processes. These methods can be implemented just after the relaxation of the collision stage in the area of the deposited particle between the deposition events to simulate the realistic density of the incident beam and accompanied long-term mass transfer processes.