In recent years subcritical multiplying structures driven by an external neutron source have been proposed for long-lived product transmutation and for safe and acceptable energy production. The study of the dynamics of these systems needs the adaptation of current methods in order to properly reproduce the peculiar features of source-driven systems.The seminars addresses the recent activities carried out by the Reactor Physics Group of Politecnico di Torino on the neutron kinetics of source-driven systems. The basic physical aspects of the time-dependent behavior of subcritical systems and their consequences on the computational methods are illustrated. The importance of transport effects on the dynamic response of a subcritical system to an external source is addressed. Recent works on the adaptation of the quasi-static technique is presented. The problem of the choice of the weighting function and its influence on the effectiveness of quasi static schemes is highlighted. Furthermore, the principles of the multipoint scheme and the possibility of its inclusion into a quasi-static framework are discussed. Some numerical results show the advantages of the technique when dealing with highly decoupled systems.