In this paper, we introduce BINet, a neural network architecture for real-time multi-perspective anomaly detection in business process event logs. BINet is designed to handle both the control flow and the data perspective of a business process. Additionally, we propose a set of heuristics for setting the threshold of an anomaly detection algorithm automatically. We demonstrate that BINet can be used to detect anomalies in event logs not only on a case level but also on event attribute level. Finally, we demonstrate that a simple set of rules can be used to utilize the output of BINet for anomaly classification. We compare BINet to eight other state-of-the-art anomaly detection algorithms and evaluate their performance on an elaborate data corpus of 29 synthetic and 15 real-life event logs. BINet outperforms all other methods both on the synthetic as well as on the real-life datasets.