Complexity theory (CT) has had a meteoric rise in management literature and the social sciences. Its fledgling importation into school leadership and management raises several questions and concerns. This article takes one view of CT and argues that, though its key elements have much to offer school leadership and management, caution has to be exercised in accepting CT too readily, as it: (1) is unclear on its own novelty, nature and status; (2) can be regarded as disguised ideology in conflating description and prescription; (3) confuses explanation with prediction; (4) is relativist, undermining its own status; (5) contains problems in its advocacy of self-organization; (6) neglects the ethical and emotional dimensions of leadership and management; and (7) risks exonerating school leaders and managers from reasonable expectations of accountability and responsibility. The article concludes that there are questions to CT at the levels of theory, ontology, deontology and ethics, but that it offers useful challenges for school leadership and management. (Contains 27 notes.)