The thesis is devoted to the studies of four birth-and-death type processes in continuum. The contact process and Glauber-type dynamics in random environment are treated. Additionally, two-component systems are introduced: the ecological model and Glauber-Potts type model. For all of the above-mentioned processes, the existence of the associated dynamics is proven. The Vlasov-type scaling is applied to the two-component models and the corresponding Vlasov equations are derived.