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There are big differences between what is complicated and what is complex. This chapter explores wat complexity is about, and in plain language terms explains the relevance for multilateral disarmament practitioners of scientific concepts like phase transitions, self/organized critacality, and complexity and network theory. Moreover, it shows how and why complexity science is relevant to understanding problems of human insecurity such as small arms proliferation, and to more effective responses. In adition, multilateral negotiations cam themselves be considered as complex social systems, which has practical implications for improving the ways in which negotiators work