In this paper, we have overviewed deterministic and stochastic approaches for the modeling of bio-molecular
reactions in systems biology. We have described and compared different versions of stochastic simulation
approaches towards the modeling of bio-molecular reaction systems, the direct approach and the family of the tauleap
methods. We also have illustrated differences between different approaches by providing numerical examples
of computational analyses for selected models. Computational examples of application of stochastic simulation
algorithms involved two systems of different interacting bio-molecular species and one model from the area of
ecology, describing interactions between two animal populations. Apart from the direct approach and tau-leap
family of methods, we have also overviewed the so called hybrid algorithm of stochastic simulations, proven to
be very efficient when there are huge differences between reaction rates in the system.