Memristors represent a transformative technology with vast potential, and their integration into microchip design, aided by artificial intelligence (AI), holds the promise of revolutionizing various industries and applications. This chapter proposes the conceptual framework for the integration of AI in microchip design using memristors. It comprehensively discusses various microchip design aspects with AI, including architectural considerations, circuit design techniques, and optimization strategies employing machine learning. The chapter also delves into its potential applications in machine learning, Internet-of-Things (IoT), robotics, healthcare, etc. Ultimately, this study contributes to the development of next-generation microchips, harnessing AI and memristor technology to revolutionize computing and technological innovation.