Computing in distributed systems increasingly occurs somewhere, with that location being integral to computational process itself. Ambient spatial intelligence (AmSI) is concerned with embedding the intelligence to respond to spatiotemporal queries and monitor geographical events in built and natural environments. The emergence of AmSI is enabled by new spatial computing technology: geosensor networks (wireless networks of sensor-enabled, location-aware computers monitoring environmental change). This chapter argues that decentralized spatial computing (DeSC), where spatial information is partially or completely filtered, summarized, or analysed in a geosensor network, is a fundamental technique required to support AmSI. By contrast, existing models for complex spatiotemporal analysis and queries almost always adopt a centralized approach to computation, where global spatial data is collated and processed, for example in a spatial database or GIS. The chapter identifies four main research challenges facing DeSC (dealing with uncertainty, dynamism, information integration, and interfaces), and illustrates the importance of DeSC to AmSI with reference to three key AmSI applications: management of the environment, infrastructure, and people. Finally, a legislative analysis of one specific domain of human activity, government acts in Australia, illustrates the potential for increasing importance of AmSI in the near future.