Abstract : This thesis broaches the study of critical phenomena in non-equilibrium systems using non-perturbative renormalisation group methods. This work is divided into two parts. The first one presents a methodological analysis of the convergence and accuracy properties of the two currently implemented approximation schemes: the derivative expansion and the field expansion. The second one is devoted to the investigation of reaction-diffusion processes. On the one hand, the first analytical determination in all dimensions of the (universal) critical exponents describing the directed percolation universality class is provided. On the other hand, the complete phase diagram of odd branching and annihilating random walks
is established and supported by numerical simulations. This analysis unveils non-perturbative effects that qualitatively alter the commonly assumed (non universal) properties of this diagram --- ensuing from perturbation theories.