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This paper reflects on the relevance of systems thinking about the interdependent policy issues bearing on the dynamics of science, technology and innovation in their relationship to economic growth. Considering the approach that characterizes much of the current economics literatures treatment of technology and growth policies, we pose the critical question: what kind of systems paradigm is likely to prove particularly fruitful in that particular problem-domain: Evolutionary, neo-Schumpeterian, and complex system dynamics approaches are conceptually attractive and we analyze their respective virtues while also acknowledging their more serious problematic features. Those become visible quickly when trying connect systems-relevant research with practical policy-making in this field. Not content to have simply identified some significant obstructions in the path toward that goal, the paper also suggests some potentially feasible ways forward.