In this introductory Chapter, we state the fundamental elements that underpin the science of creative thinking, recognizing at the same time that we are following a path towards the establishment of that science, and that many challenges are yet to be met. Considering theoretical models for the creative thinking process, we dis-cuss the minimum number of stages, the concept of optimal originality, and we review the most important existing models, outlining their features and limita-tions. The discussion then moves from the individual to the social level. After reviewing the generally accepted approaches in social creativity analysis, we call for balanced fusion of the individual and social points of view, avoiding artificial contrasts. Two macro domains are then analysed: engineering & design and art. In the former, we introduce the concepts of creative reproduction of nature, extension of capabilities and of conditions for life, and we discuss the use of metaphors in various forms. For the latter, we start with a scientific definition of inspiration, then move on to discuss the delicate balance between discipline and spontaneity in artistic education. Also, we touch upon the state-of-the-art of artificial creators that can produce mimicking the style of great artists. We conclude the Chapter by ad-dressing some areas which we consider to be both urgent and necessary in the de-velopment of the science of creative thinking.
