Stochastic dynamics describes processes in complex systems having the probabilistic nature.They can involve very different dynamical systems and occur on very different temporal and spatial scale. This paper discusses the concept of stochastic dynamics and its implementation in the popular program MBN Explorer. Stochastic dynamics in MBN Explorer relies on the Monte Carlo approach and permits simulations of physical, chemical and biological processes. The paper presents the basic theoretical concepts underlying stochastic dynamics implementation and provides several examples highlighting its applicability to different systems, such as diffusing proteins seeking an anchor point on a cell membrane, deposition of nanoparticles on a surface leading to structures with fractal morphologies and oscillations of compounds in an autocatalytic reaction. The chosen examples illustrate the diversity of applications that can be modeled by means of stochastic dynamics with MBN Explorer.