We present a short introduction into the framework of piecewise deterministic Markov processes and illustrate it with examples related to biological models: dispersal of biological systems, cell cycle, structured populations, regulatory networks, as well as neural activity. Their distributions are described by semigroups of operators on the space L¹ (stochastic semigroups). We start with a new general result on asymptotic decomposition of stochastic semigroups. Then we present some corollaries useful in studying of dynamical systems with random switching. We illustrate mathematical results by applications to gene expression models.