Various novel effects in nanostructures of magnetic atoms exchange-coupled to a metallic system of conduction electrons are reviewed. To this end we discuss analytical results and numerical data obtained by the density-matrix renormalization group and the real-space dynamical mean-field theory for the multi-impurity Kondo model. This model hosts complex physics resulting from the competition or cooperation of different mechanisms, such as the Kondo effect, the RKKY indirect magnetic exchange, finite-size gaps and symmetry-induced degeneracies in the electronic structure of finite metallic systems, quantum confinement in the strong-coupling limit, and geometrical frustration.