Creativity has been studied as a psychological phenomenon and research has focused on factors that influence the human variability and acquisition of such capacity. Still, the creative process remained metaphorically described, and with no rigorous formalization. Moreover, the knowledge background of ideation has been ignored, as well as the interplay between creative ideation and knowledge generation. This paper is an introduction to recent advances in design theory, namely C-K theory or Concept Knowledge theory (Hatchuel and Weil 2003, 2009), that overcomes such biases and assumes that creative thinking can be formally described with solid theoretical premises that can be experimentally tested. There is now a significant literature that assesses its propositions, findings and implications. C-K theory introduces new notions: " concept undecidability " , " knowledge independence " , " generic expansions " and " Knowledge reordering " ; they capture key necessary mechanisms of any creative process. Therefore, classic interpretations of creativity (association of ideas, analogy, blending, divergence and convergence) have to be revisited. C-K theory shows that they account for some aspects of ideation, but miss important operators that uncover the generative and expanding logic of creative thinking. It also reveals that specific knowledge structures are needed to allow for creative generation. C-K theory captures within the same formal model, both creative ideation and learning, invention and discovery, fixation and expansion of knowledge. Thanks to its explanatory and predictive power, C-K theory allows a new articulation between theory and observation in the field of creativity. Several findings have confirmed the value of such research potential. Finally, C-K theory stimulates transdisciplinary research through the development of a rigorous design science and the modelling of creative logic in all disciplines.