The topic of dynamical systems in spaces of measures is gaining interest over the last couple of years. In the lecture we will provide examples and motivation for considering such a framework. One is purely deterministic: originating from crowd dynamics and the analysis of the behavior of interacting particle systems. Another is concerned with systems in which deterministic behavior is alternated randomly with random interventions. The latter type of problems are motivated by the modeling of particular biological processes, e.g. gene expression. In the analysis of the resulting models in spaces of measures one encounters new interesting mathematical issues. Some of these will be discussed in the lecture.