Artificial intelligence systems are increasingly becoming a component of security-critical applications. The protection of such systems from various types of destructive influences is thus a relevant area of research. The vast majority of previously published works are aimed at reducing vulnerability to certain types of disturbances or implementing certain resilience properties. At the same time, the authors either do not consider the concept of resilience as such, or their understanding varies greatly. This work presents a formalized definition of resilience and its characteristics for artificial intelligence systems from a systemic point of view. It systematizes ideas and approaches to building resilience to various types of disturbances. Taxonomy of resilience of artificial intelligence systems to destructive disturbances is proposed. Approaches and technologies for complex protection of intelligent systems, issues of their resource efficiency and other open research issues are considered. Approaches of resilience assessment for artificial intelligence system are also analyzed and recommendations are provided for their implementation.