The main results of theoretical investigations and computer simulations of a plasma expansion with dust particles as well as the methods used in these investigations are presented in this short review. The hydrodynamic treatment consists of the set of fluid equations for the dust particles and the equation for the dust particle charge according to the orbit limited probe theory. The kinetic treatment consists of the Vlasov equation for dust particles with constant charge together with Boltzmann distributions with constant temperature for the electrons and ions and the condition of quasi-neutrality. Computer simulations are described in the framework of the PIC method taking into account the dynamics of the dust particle charge as well as Coulomb collisions of electrons and ions with dust particles. The results of these investigations show the essential influence of dust particles on the plasma expansion. In particular, dust particles cause the distributions of electrons and ions to deviate from equilibrium due to their selective collection by dust particles.