As a purposive sustainability transition requires environmental innovation and innovation policy, we discuss potentials and limitations of three dominant strands of literature in this field, namely the multi-level perspective on socio-technical transitions (MLP), the innovation systems approach (IS), and the long-wave theory of techno-economic paradigm shifts (LWT). All three are epistemologically rooted in an evolutionary understanding of socio-technical change. While these approaches are appropriate to understand market-driven processes of change, they may be deficient as analytical tools for exploring and designing processes of purposive societal transformation. In particular, we argue that the evolutionary mechanism of selection is the key to introducing the strong directionality required for purposive transformative change. In all three innovation theories, we find that the prime selection environment is constituted by the market and, thus, normative societal goals like sustainability are sidelined. Consequently, selection is depoliticised and neither strong directionality nor incumbent regime destabilisation are societally steered. Finally, we offer an analytical framework that builds upon a more political conception of selection and retention and calls for new political institutions to make normatively guided selections. Institutions for transformative innovation need to improve the capacities of complex societies to make binding decisions in politically contested fields.