Understanding atomistic diffusion and relaxation mechanisms remains one of the main challenges of materials science both at the experimental and numerical levels. Over the years, a number of very interesting simulation approaches have been introduced to lift this limitation. In this talk, I present the kinetic Activation-Relaxation Technique (k-ART),
an off-lattice kinetic Monte Carlo algorithm with on-the-fly catalog building. This method brings together the activation-relaxation technique (ART nouveau), an efficient open-ended transition-state searching algorithm, NAUTY, a topological-analysis code and the KMC algorithm. Combining these approaches, k-ART is able to follow atomistic kinetic in complex materials, including ion-bombarded systems, semiconductor and metallic alloys, defective and disordered materials, etc., over more than 10 decades in time, reaching the second time scale and more. In addition to describing the algorithm, I will present recent applications to carbon diffusion in iron, relaxation of ion bombarded silicon, defect diffusion in amorphous materials and more.