- Self-organization processes leading to pattern formation phenomena are ubiquitous in nature. Intensive theoretical and experimental research efforts during the past few decades have resulted in a mathematical theory of pattern formation whose predictions are well confirmed by controlled laboratory experiments. There is an increasing observational evidence that pattern formation plays a significant role in shaping dryland landscapes. Supporting these observations are studies of continuum vegetation models that have reproduced many of the observed patterns. Such continuum models consist of partial differential equations and lend themselves to the powerful methods of pattern formation theory. Indeed, vegetation pattern formation has been identified with mathematical instabilities of uniform vegetation states, occurring at threshold degrees of aridity. This paper describes applications of this modelling approach to problems in landscape, community, ecosystem and restoration ecology, highlighting new open questions and research directions that are motivated by pattern formation theory. Three added values of this approach are emphasized: (i) the approach reveals universal nonlinear elements for which a great deal of knowledge is already available, (ii) it captures important aspects of ecosystem complexity, and (iii) it provides an integrative framework for studying problems in spatial ecology.