This chapter explores the transformative shift in human–computer relationships driven by generative artificial intelligence (AI). Moving beyond traditional Human–Computer Interaction (HCI) frameworks focused on task completion and efficiency, this chapter delves into Human–Computer Creativity (HCC), where AI systems act as co-creators rather than passive tools. Through advancements in generative models, AI enables a collaborative environment that fosters creativity in diverse fields, including education, art, and healthcare. By examining the historical progression of HCI, the capabilities of generative AI, and its applications, the chapter illuminates the paradigm shift from interaction to co-creation. Key themes include the evolving roles of humans and AI, ethical considerations, and the comparative analysis of interaction-based and creativity-based human–computer models. This shift highlights the potential of generative AI to reshape our understanding of creativity, challenging traditional notions of authorship and originality. In sum, the chapter provides a comprehensive analysis of how generative AI enhances and redefines human creativity, offering insights into the future of human–computer collaboration.