An overview is given of recent work on the decay of two-dimensional clusters on a Ag(111) surface. Experimental studies using scanning tunnelling microscopy are presented, and various approaches to extract quantitative information on the relevant atomic processes from cluster decay experiments are discussed. It is shown that for typical surface morphologies, the decay rate of individual clusters depends critically on their local environment. Quantitative analysis therefore generally requires complex and detailed case-by-case modelling involving numerical methods. This difficulty can be overcome experimentally by preparing well-defined model structures for which an analytical description can be used without any loss of accuracy. (C) 1998 Elsevier Science B.V. All rights reserved.