In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly using Voronoi models and similar complexes (both euclidean and hermitian). We will describe in details the geometric, cohomological and topological tools, as well as Hecke actions on the cohomology of modular groups and asymptotic results. Applications to number theory and K-theory will also be detailled. We will also explain several computational methods and algorithmic improvements in order to get explicit results.The last part of the lectures will be dedicated to open problems.