The recent renewed interest on fluid-fuel nuclear systems has stimulated the development of models and methods for the physics of these systems, for both steady-state and transient analysis. The European research project MOST within the 5-th Framework Program has devoted a considerable effort to the assessment of models and computational tools for molten-salt systems. The seminar addresses the activities carried out at Politecnico di Torino on the neutronics of fluid-fuel systems. The basic physical phenomena connected to the motion of the fuel in a nuclear reactor are illustrated. Suitable mathematical models for the proper description of the neutronics are presented, showing the peculiar effects of the velocity field on the steady-state distribution and the time-dependent response for a molten salt reactor, both critical and subcritical. The second part of the seminar is devoted to the deduction of the quasi-static technique for fluid-fuel systems, extending the classic factorization methods. Results obtained in the recent benchmark exercise performed within the MOST Projects are presented.