This article deals with the IT security of connectionist artificial intelligence (AI) applications, focusing on threats to integrity, one of the three IT security goals. Such threats are for instance most relevant in prominent AI computer vision applications. In order to present a holistic view on the IT security goal integrity, many additional aspects such as interpretability, robustness and documentation are taken into account. A comprehensive list of threats and possible mitigations is presented by reviewing the state-of-the-art literature. AI-specific vulnerabilities such as adversarial attacks and poisoning attacks as well as their AI-specific root causes are discussed in detail. Additionally and in contrast to former reviews, the whole AI supply chain is analysed with respect to vulnerabilities, including the planning, data acquisition, training, evaluation and operation phases. The discussion of mitigations is likewise not restricted to the level of the AI system itself but rather advocates viewing AI systems in the context of their supply chains and their embeddings in larger IT infrastructures and hardware devices. Based on this and the observation that adaptive attackers may circumvent any single published AI-specific defence to date, the article concludes that single protective measures are not sufficient but rather multiple measures on different levels have to be combined to achieve a minimum level of IT security for AI applications.