We discuss how the anomalous increase of the viscosity in colloidal systems with short-range attraction can be related to the formation of long-living clusters. Based on molecular dynamics and Monte Carlo numerical simulations of different models, we propose a similar picture for colloidal gelation at low and intermediate volume fractions. On this basis, we analyze the distinct role played by the formation of long-living bonds and the crowding of the particles in the slow dynamics of attractive colloidal systems.