IT systems of today are becoming larger and more complex, rendering their human supervision more difficult. Artificial Intelligence for IT Operations (AIOps) has been proposed to tackle modern IT administration challenges thanks to AI and Big Data. However, past AIOps contributions are scattered, unorganized and missing a common terminology convention, which renders their discovery and comparison impractical. In this work, we conduct an in-depth mapping study to collect and organize the numerous scattered contributions to AIOps in a unique reference index. We create an AIOps taxonomy to build a foundation for future contributions and allow an efficient comparison of AIOps papers treating similar problems. We investigate temporal trends and classify AIOps contributions based on the choice of algorithms, data sources and the target components. Our results show a recent and growing interest towards AIOps, specifically to those contributions treating failure-related tasks (62%), such as anomaly detection and root cause analysis.