A well known model in Stochastic Geometry is the Boolean model where balls are located at random in space and their union is investigated. The Vietoris-Rips and the Cech complex reflect the topological structure of the Boolean model. We are interested in concentration inequalities for the number of k-dimensional simplices of this simplicial complexes or more general subgraph counts. This gives rise to concentration inequalities for component counts. In the last part of the talk we investigate the Betti numbers of components of these simplicial complexes.