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In the last decades, the management of innovation has achieved increasing importance in both academic and business environments. For the companies, an effective engagement in innovation efforts involves the adoption of management models to guide the definition of organizational processes to conduct innovation opportunities throughout the organization. In this context, graphical representations can strongly communicate the central propositions of each model, accelerating the diffusion and influence of such models in both academic and business environments. Based on an academic database search, and snowball procedure, models were selected considering the unique characteristics of their graphical representation. This article contributes to the knowledge in the field by proposing a typology of innovation management models, highlighting model's biases, gaps, strengths and weaknesses, and by identifying important tensions among models that spillover to the innovation management field in both research and practice. This article discusses conflicts regarding the limits of the innovation process (events that start and end the process and complementary approaches), the limits of focusing on processes, the differentiation of research and development and new product development activities. In the end, the article addresses emerging approaches related to radical innovation, design thinking and startups, and stresses contributions for research and practice.