The growth of metals and semiconductors on reconstructed semiconductor surfaces proceeds through a number of conceptually distinct stages. These include: 1) the growth of the first layer or layers, which may have different reconstructions as growth proceeds; 2) the growth of (2D or 3D) islands of the deposit, and/or by step flow; 3) coalescence and/or coarsening of islands and/or the introduction of defects such as dislocations. Of particular interest are cases when the different ‘stages’ are in competition with each other, i.e. they constitute alternative sinks for (and sources of) arriving and migrating adatoms. The development of rate equations to describe such situations, and extract relevant atomic parameters, is outlined. Experimental examples are taken from recent work on Ag and Ge deposits on Si( 111) and (100) surfaces.