Résumé : Society is transforming through a whirlpool of innovations. This includes technological as well as social innovations, i.e. changes in social relations involving new ways of doing, organizing, framing and knowing. Especially the potentials for transformative social innovation (TSI) are gaining the interest of progressive political actors and critical scholars. Occurring in the form of new modes of governance and alternative ways of working and living together, TSI involves the challenging, altering or replacing of dominant institutions. As documented in various strands of critical social inquiry and innovation research, TSI praxis is pervaded with contradictions, anomalies and paradoxes. This methodological contribution addresses the challenge that tends to remain: How to elaborate this general critical awareness into more operational ‘strategies of inquiry’? The paper discusses paradoxes of a) system reproduction, b) temporality, and c) reality construction. Identifying distinct kinds of contradictions and distinct empirical phenomena, this differentiation also calls attention to the associated differences between realist, processual and constructivist research philosophies. Gathering the empirical analyses, theoretical interpretations and methodological advances that have been made on these paradoxes, this contribution opens up the scope for critical and practically relevant innovation research: It is important to bridge the divide between rigorous but sterile methodological know-how, and critical-reflexive theorizing that lacks operational insights.