Event-based vision, characterized by low redundancy, focus on dynamic motion, and inherent privacy-preserving properties, naturally fits the demands of video anomaly detection (VAD). However, the absence of dedicated event-stream anomaly detection datasets and effective modeling strategies has significantly hindered progress in this field. In this work, we take the first major step toward establishing event-based VAD as a unified research direction. We first construct multiple event-stream based benchmarks for video anomaly detection, featuring synchronized event and RGB recordings. Leveraging the unique properties of events, we then propose an EVent-centric spatiotemporal Video Anomaly Detection framework, namely EWAD, with three key innovations: an event density aware dynamic sampling strategy to select temporally informative segments; a density-modulated temporal modeling approach that captures contextual relations from sparse event streams; and an RGB-to-event knowledge distillation mechanism to enhance event-based representations under weak supervision. Extensive experiments on three benchmarks demonstrate that our EWAD achieves significant improvements over existing approaches, highlighting the potential and effectiveness of event-driven modeling for video anomaly detection. The benchmark datasets will be made publicly available.