Anomalies are unusual and significant changes in a network's traffic levels, which can often involve multiple links. Diagnosing anomalies is critical for both network operators and end users. It is a difficult problem because one must extract and interpret anomalous patterns from large amounts of high-dimensional, noisy data. In this talk I will propose the subspace method to diagnose anomalies. This diagnosis technique is based on a separation of the high-dimensional space occupied by a set of network traffic measurements into disjoint subspaces corresponding to normal and anomalous network conditions. Using only simple traffic measurements from links, the subspace method can: (1) accurately detect when a volume anomaly is occurring; (2) correctly identify the underlying origin-destination (OD) flow which is the source of the anomaly; and (3) accurately estimate the amount of traffic involved in the anomalous OD flow. I will evaluate the method's ability to diagnose (i.e., detect, identify, and quantify) both existing and synthetically injected volume anomalies in real traffic from two backbone networks. We find that the subspace method consistently diagnoses the largest volume anomalies, and does so with a very low false alarm rate. Finally, if time permits, I will present recent characterization results on the nature and cause of traffic anomalies.