Integrated sensing and communication (ISAC) is a promising technique to increase spectral efficiency and support various emerging applications by sharing the spectrum and hardware between these functionalities. However, the traditional ISAC schemes are highly dependent on the accurate mathematical model and suffer from the challenges of high complexity and poor performance in practical scenarios. Recently, artificial intelligence (AI) has emerged as a viable technique to address these issues due to its powerful learning capabilities, satisfactory generalization capability, fast inference speed, and high adaptability for dynamic environments, facilitating a system design shift from model-driven to data-driven. Intelligent ISAC, which integrates AI into ISAC, has been a hot topic that has attracted many researchers to investigate. In this paper, we provide a comprehensive overview of intelligent ISAC, including its motivation, typical applications, recent trends, and challenges. In particular, we first introduce the basic principle of ISAC, followed by its key techniques. Then, an overview of AI and a comparison between model-based and AI-based methods for ISAC are provided. Furthermore, the typical applications of AI in ISAC and the recent trends for AI-enabled ISAC are reviewed. Finally, the future research issues and challenges of intelligent ISAC are discussed.