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Spatial abstractions promise to be basic necessary ingredients for a novel “spatial computing” approach to distributed systems development and management, suitable to tackle the complexity of modern distributed computing scenarios and promoting self-organization and self-adaptation. In this paper, we analyze the key concepts underlying spatial computing and show how they can be organized around a sort of “spatial computing stack”, in which a variety of apparently very diverse mechanisms and approaches can be properly framed. Following, we present our current research work on the TOTA middleware as a representative example of a general-purpose approach to spatial computing. In particular, we discuss how TOTA can be exploited to support the development and execution of self-organizing and self-adaptive spatial computing applications.