The 40th birthday of the Schumpeter Society offers an excellent chance to reflect on Schumpeter intellectual heritage, as well as its shortcomings and the subsequent developments. No doubt that reference to Schumpeter has been a precious shortcut to the rediscovery of the crucial importance of innovation for economic dynamics. However, such a rediscovery may be the harbinger of a fuller appreciation of the economy as a complex evolving system, or, on the contrary, be reincorporated into an enlarged canonic ‘equilibrium’ paradigm. The bifurcation concerns the domains of measurement (including the appropriate statistics and econometrics), modelling, and finally, policies. In this work, we discuss such crossroads, the dangerous twists that the Schumpeter-inspired tradition has taken, together with some promising evolutionary alternatives.