In this paper we identify a tension between the discourse around managing temporary assignments focused on producing innovative outcomes, that is, the discourse related to projects and project management, and the emerging understanding of innovation processes, as captured by the concept of interactive innovation.Contrasting the project management discourse with what we now understand about innovation processes in practice, especially those that are radical and, or disruptive, provides explanatory power for some of the significant problems and overall high failure rates (as measured, for example, in terms of the triple constraint of time, budget and scope) often associated with these innovation projects. We illustrate this tension between the discourse on projects and project management and the realities of interactive innovation processes with an example from biomedicine. In the discussion we explore why this tension exists, focusing on explanations that consider organizational ambidexterity and situate projects in their broader institutional context.