This paper presents a novel approach to deal with dynamic and highly uncertain traffic in dynamic network scenarios. The Reactive Robust Routing (RRR) approach is introduced, a combination of proactive and reactive techniques to improve network efficiency and robustness, simplifying network operation. RRR optimizes routing for normal-operation traffic, using a time-varying extension of the already established Robust Routing technique that outperforms the stable approach. To deal with anomalous and unexpected traffic variations, RRR uses a fast anomaly detection and localization algorithm that rapidly detects and localizes abrupt changes in traffic flows, permitting an accurate routing adaptation. This algorithm presents well-established optimality properties in terms of detection/localization rates and localization delay, which allows for generalization of results, independently of particular evaluations. The algorithm is based on a novel parsimonious model for traffic demands which allows for detection of anomalies using easily available aggregated-traffic measurements, reducing the overheads of data collection.