This paper explores how 'creativity' and 'innovation' are most usefully modelled for the modern design context invariably consisting of conflicting technical, economical, organisational and social demands. Section 2 summarises the experiences and observations of engineers and the most comprehensive theories of creativity and innovation proposed by psychologists and educators, which set the stage for a generic model. Section 3 evaluates and synthesises the scope and use of over 100 commercially available tools to enhance creativity and innovation. We place this in the context of the 'processes of creating' outlined in the psychological literature as well as those generally accepted to lead to internationally competitive outcomes in engineering, business, sociology and literature, among others. The series of tables defines a preliminary Taxonomy of Tools to enable potential users to clarify how and where additional information or help should be solicited, to streamline any stage of engineering design. Section 4 elucidates a 'process of creating' as a generic model, which illustrates how contradictory input data become novel outcomes in processes that co-evolve the bodies of knowledge on both sides of a problem–solution equation. The model, in contrast to previous theories, is not vague – apparent contradictions between design demands can be resolved in precise steps, as long as the starting point of all actors/stakeholders is made coincident.