C-K theory has been developed by Armand Hatchuel and Benoit Weil and then by other researchers since 1990s. In this paper we show that its very abstract nature and its high degree of universality actually supported a large variety of industrial applications. We distinguish three types of applications: 1) C-K theory provides a new language, that supports new analysis and descriptive capacity and new teachable individual models of thoughts; 2) C-K theory provides a very general framework to better characterize the validity domain and the performance conditions of existing methods, leading to potential improvement of these methods ; 3) C-K theory is the conceptual model at the root of new design methods that are today largely used in the industry.