Advances in Artificial Intelligence (AI) have influenced almost every field including computer science, robotics, social engineering, psychology, criminology and so on. Although AI has solved various challenges, potential security threats of AI algorithms and training data have been stressed by AI researchers. As AI system inherits security threats of traditional computer system, the concern about novel cyberattack enhanced by AI is also growing. In addition, AI is deeply connected to physical space (e.g. autonomous vehicle, intelligent virtual assistant), so AI-related crime can harm people physically, beyond the cyberspace. In this context, we represent a literature review of security threats and AI-related crime. Based on the literature review, this article defines the term AI crime and classifies AI crime into 2 categories: AI as tool crime and AI as target crime, inspired by a taxonomy of cybercrime: Computer as tool crime and Computer as tool crime. Through the proposed taxonomy, foreseeable AI crimes are systematically studied and related forensic techniques are also addressed. We also analyze the characteristics of the AI crimes and present challenges that are difficult to be solved with the traditional forensic techniques. Finally, open issues are presented, with emphasis on the need to establish novel strategies for AI forensics.