Recent decades have revealed a gap between promises and realities of accountability in education governance, as well as further afield. Despite efforts identifying and analysing cautionary tales of accountability interventions, a systematic approach to support progressive improvements for managing accountability in complex education systems is yet to be widely adopted. This review of the interdisciplinary literature leverages the complexity paradigm to address the extant lack of clarity in theory and practice surrounding accountability. Central to this are recent research efforts that embrace accountability's foundations as a relational exchange of accounts. The approach enables distancing accountability from misconceptions arising from its patchy track record in practice and the rhetorical usage of the term. The review discusses implications for understanding and managing accountability within contemporary strategic governance. In such an environment, this means rethinking the management of accountability stresses by practitioners as a new normal to be grappled with -- and where possible attenuated -- rather than the object of tractable solutions, as has been mistakenly conceived in the past.