Process philosophy has drawn attention to the world as ambiguous and ever changing, however also enactable. This makes entrepreneurship a processual phenomenon, rightly addressed as ‘entrepreneuring’. Recognizing not only their cognitive, yet also affective and conative capabilities, makes it possible for human actors to mobilize forces that bring the world to a standstill long enough to create a venture for value creation. This, however, calls for the insight that is different to universal scientific knowledge – episteme and techne – namely, the situated insights that Aristotle addressed as mētis and phronesis. Mētis then concerns alertness and shrewdness and phronesis is about prudence in the context of action. Academic education can only provide these competencies needed to train for entrepreneuring by letting the students travelling across the boundaries of the university. In addition, the dominance of management as an ideology must be proactively dealt with. Three cases in academic training for entrepreneuring, all in the Swedish context, which show radically different ways of dealing with these challenges, are presented in a comparative analysis. The lessons are summarized in general conditions for providing training that advances entrepreneurship students’ situated and actionable insights.