In this work we develop a new approach to monitoring origin-destination flows in a large network. We start by building a state space model for OD flows that is rich enough to fully capture temporal and spatial correlations. We apply a Kalman filter to our linear dynamic system that can be used for both estimation and prediction of traffic matrices. We call our system a traffic matrix tracker due to its lightweight mechanism for temporal updates that enables tracking traffic matrix dynamics at small time scales. Our Kalman filter approach allows us to go beyond traffic matrix estimation in that our single system can also carry out traffic prediction and yield confidence bounds on the estimates, the predictions and the residual error processes. We show that these elements provide key functionalities needed by monitoring systems of the future for carrying out anomaly detection. Using real data collected from a Tier-1 ISP, we validate our model, illustrate that it can achieve low errors, and that our method is adaptive on both short and long timescales.