We present a geometric formulation for thermodynamical systems out of equilibrium, which extends the Lagrangian and Hamiltonian formulations of classical mechanics and field theory to include irreversible processes in discrete and continuum systems. The irreversibility is encoded into a nonlinear nonholonomic constraint given by the expression of the entropy production associated to the irreversible processes involved in the system. We show that the evolution equations for nonequilibrium thermodynamics admit an intrinsic formulation in terms of Dirac or multi-Dirac structures. We explain why this geometric approach is useful for the modelling of nonequilibrium systems and for the design of geometry preserving numerical discretization. This is a joint work with H. Yoshimura.