In this paper we discuss m athem atical, num erical and atom istic models of grow th a t surfaces through a num ber of exam ples. I t is shown how such models have often been successful in predicting the stru ctu res th a t are observed experim entally. D ifferent kinds of models are often com plem entary to each other. M athem atical models can give guidance on the long-tim e behaviour of th e system b u t often need help from more detailed sim ulation to decide w h at to assum e ab o u t th e

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... underlying microscopic processes. D espite their success, such models still have a long w ay to go. In p articular, they need to address the question of how to predict th e effective properties of coatings. H ere experim ental d a ta are n ot always available, and guidance from theory is greatly needed.