Innovation ambidexterity has emerged as a primary interest in management research due to the strategy’s support for adaptability and flexibility pursuant to competitiveness. While management studies investigate and explicate the socioeconomic and technological challenges of ambidexterity, there is a gap in knowledge on the determinants that underpin the management of ambidextrous organisations. To tackle this paucity, this article uses a systematic approach to review existing literature on innovation ambidexterity, identifying the main determinants for managing ambidexterity in organisations, and setting an agenda for future management research informed by these determinants. The review assembles and critically appraises 121 articles published between 2007 and 2021. It examines the research clusters, investigated industry sectors, research methodologies, management theories, and research contributions of studies on innovation ambidexterity. The review finds seven main determinants for managing ambidexterity consisting of: (i) process mechanisms, (ii) organisational learning, (iii) leadership styles, (iv) technology investments, (v) organisational contexts, (vi) environmental uncertainties, and (vii) institutional pressures. Using insights from the review process, the article proposes a set of management priorities and suggests seven areas for future ambidexterity research with respect to digital interdependence, organisational legacy, stewardship behaviour, technology sourcing, organisational resilience, environmental readiness, and institutional transformation. Theoretically, the article contributes to knowledge via a multi-level ‘wheel’ model of ambidexterity management that links management determinants to priorities, and managerially, the review offers a fresh perspective on management factors for ambidexterity.