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Innovation economics is poorly defined due to a plethora of meanings to innovation, and each having a distinctive diverse connection to economic analysis. This crucial aspect of economic development is only weakly integrated into the main body of economics. An excursion through the history of economic thought is conducted in order to find the innovative entrepreneur. This starts with early political economy and on to the cul-de-sac of neoclassical economics and then the early 20th Century dynamic paths for innovation of Joseph Schumpeter (from supply-side) and Michał Kalecki (from demand-side). The tour ends with the innovation systems work of a diverse set of modern heterodox economists. There is a lack of coherence on what innovation economics is, and the role of the innovative entrepreneur as the change agent tends to fade in the background of these complex innovation systems. A research strategy to overcome this problem ends the paper.