We present a detailed budget of the changes in atmospheric aerosol mass and numbers due to various processes: emission (including instant condensation of soluble biogenic emissions), nucleation, coagulation, H<sub>2</sub>SO<sub>4</sub> condensation and in-cloud production, aging and deposition. The budget is created from monthly averaged tracer tendencies calculated by the global aerosol model ECHAM5.5-HAM2 and allows us to investigate process contributions at various length-scales and timescales. As a result, we show in unprecedented detail what processes drive the evolution of aerosol. In particular, we show that the processes that affect aerosol masses are quite different from those that affect aerosol numbers. Condensation of H<sub>2</sub>SO<sub>4</sub> gas onto pre-existing particles is an important process, dominating the growth of small particles in the nucleation mode to the Aitken mode and the aging of hydrophobic matter. Together with in-cloud production of H<sub>2</sub>SO<sub>4</sub>, it significantly contributes to (and often dominates) the mass burden (and hence composition) of the hydrophilic Aitken and accumulation mode particles. Particle growth itself is the leading source of number densities in the hydrophilic Aitken and accumulation modes, with their hydrophobic counterparts contributing (even locally) relatively little. As expected, the coarse mode is dominated by primary emissions and mostly decoupled from the smaller modes. Our analysis also suggests that coagulation serves mainly as a loss process for number densities and that, relative to other processes, it is a rather unimportant contributor to composition changes of aerosol. The analysis is extended with sensitivity studies where the impact of a lower model resolution or pre-industrial emissions is shown to be small. We discuss the use of the current budget for model simplification, prioritization of model improvements, identification of potential structural model errors and model evaluation against observations.