SUMMARYThis special issue contains selected high-quality papers from the invited lectures of the Fourth International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives (FVCA), which was sponsored by Marrakech University of Science and Technology in Morocco and held in the university on July 4-8, 2005. The FVCA symposia series aims to provide an international and privileged forum for the exchange and profitable discussions bringing together mathematicians, physicists and engineers concerned with finite volume techniques in both theory and practice. Indeed, the finite volume method is nowadays adopted by a broad base of the scientific community including those concerned with the use of numerical simulations in the resolution of complex physical problems in industry, civil engineering and the environmental.This special issue contains six papers based on those that were presented as invited lectures at FVCA4. Particular attention is focused on convergence, error analysis and new fields of application. Chainais-Hillairet's [1] talk was devoted to the drift-diffusion and the energy transport models appearing in the modelling of semiconductor devices. The main difficulty arising in the approximation of the energy transport model using finite volume schemes is the discretization of the Joule heating term in the equation for the density of energy. Following some recent ideas by K. Domelevo and P. Omnes for the discretization of the Laplace equation on almost general meshes, Chainais-Hillairet explains the construction of a finite volume approximation of the * Correspondence to: Nigel P. Weatherill, College of Engineering and Physical Sciences,