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By adopting a semiparametric approach, the ‘traditional’ regional knowledge production function is developed in three complementary directions. First, the model is augmented with region-specific time trends to account for endogeneity due to selection on unobservables. Second, the nonparametric part of the model relaxes the standard assumptions of linearity and additivity regarding the effect of R&D and human capital. Finally, the assumption of homogeneity in the effects of R&D and human capital is also relaxed by explicitly accounting for the differences between developed and lagging regions. The analysis of the genesis of innovation in the regions of the European Union unveils nonlinearities, threshold effects, complex interactions and shadow effects that cannot be uncovered by standard parametric formulations.