  Understanding and control of cluster and thin film growth on solid surfaces
is a subject of intensive research to develop nanomaterials with new physical
properties. In this Colloquium we review basic theoretical concepts to describe
submonolayer growth kinetics under non-equilibrium conditions. It is shown how
these concepts can be extended and further developed to treat self-organized
cluster formation in material systems of current interest, such as nanoalloys
and molecular clusters in organic thin film growth. The presentation is focused
on ideal flat surfaces to limit the scope and to discuss key ideas in a
transparent way. Open experimental and theoretical challenges are pointed out.
