This proceedings-like contribution presents the results obtained during and after (as an output of) the CEMRACS summer research center held at CIRM in Luminy in 2003. The brief was to study problems arising in kinetic and hyperbolic theory from a numerical point of view. This includes a wide variety of industrial and engineering problems, including multi-phase flows, plasma physics problems, quantum particle dynamics, radiative transfer, sprays and aero-acoustics. From a mathematical point of view, in altogether 14 contributions, we learn about problems connected with numerical solutions of the Vlasov equation, the nonlinear Schrödinger equation, the conservative bifluid model, two-phase flows and phase transition modeling, etc. As to the numerical methods used, the authors solve the problems listed above generally by Particle-In-Cell methods and the time splitting spectral scheme (kinetic problems), and explicit finite volume methods and the discontinuous Galerkin method (hyperbolic problems). This contribution will be valuable for researchers, engineers and graduate students seeking information on the topic.