In this tutorial review we summarize the standard approaches to describe aerosol formation from atmospheric vapours and subsequent growth - with a particular emphasis on the interplay between equilibrium thermodynamics and non-equilibrium transport. We review the use of thermodynamics in describing phase equilibria and formation of aerosol particles from supersaturated vapour via nucleation. We also discuss the kinetics of cluster formation and transport phenomena, which are used to describe dynamic mass transport between the gaseous and condensed phases in a non-equilibrium system. Finally, we put these theories into the context of atmospheric observations of aerosol formation and growth.