Satellite radar interferometry (InSAR) is a precise and efficient technique to monitor deformation on Earth with millimeter precision. Most InSAR applications focus on geophysical phenomena, such as earthquakes, volcanoes, or subsidence. Monitoring civil infrastructure with InSAR is relatively new, with potential for operational applications, but currently not exploited to full advantage. Here we investigate how to optimally assess and monitor the structural health of civil infrastructure using InSAR, and develop methodology to improve its capability for operational monitoring. InSAR kinematic time series analysis involves the processing of extremely large datasets to estimate the relative movements of points on the infrastructure. The estimated movements may expose strain in the structure, potentially revealing structural health problems. However, the optimal mathematical model relating the satellite observations to the kinematic parameters of interest is unknown. We propose multiple hypothesis testing as a means to identify the most probable mathematical model. For each target, the null-hypothesis of ‘steady-state’ motion is considered as default, which is tested against a multitude of potential temporal models, built based on a library of canonical functions. If the null hypothesis is sustained, there is no (significant) anomaly in the data. If the null hypothesis is rejected, we test the entire library of potential alternative models with different physically realistic parameters against the null hypothesis using the B-method of testing. Finally, using test-ratios, we select the most likely model for each target, update the quality description of the estimates, while avoiding overfitting. InSAR processing strategies are designed and implemented for structural health assessment of railway infrastructure and buildings. The Qinghai-Tibet railway, at 5000m altitude, is suspected to be affected by dynamic changes in permafrost environments. Using medium resolution SAR data, we apply an ‘all-pixel’ approach based on statistical similarity to tackle geometric decorrelation and maximize the density of InSAR measurement points over the track. Seasonal changes in deformation are detected, most likely due to freezing and thawing of the permafrost’s active layer. To explore the capability of railway infrastructure monitoring using multi-track high-resolution SAR data, we estimate the 3D temporal behavior of the Betuwe railway, the Netherlands, in a track-fixed reference system in the transversal, longitudinal, and normal direction using 248 TerraSAR-X images acquired from ascending and descending orbits. For building monitoring, we study a shopping mall in Heerlen, the Netherlands. Due to a developing sinkhole below, the building lost its structural support, leading to a sudden evacuation and a near-collapse. Using consecutive InSAR data time series acquired by four different SAR satellites between 1992 and 2011, we find significant precursory motion. We integrate these InSAR data time series and improve the precision of geolocation of the InSAR measurement points using additional lidar-based data. The detected localized strain appears to be related to an upward migrating cavity. The analysis demonstrates the feasibility of an early detection of anomalous processes in the underground. This study reveals the high potential of structural health monitoring using observations from satellites, either for forensic analysis—investigating the behavior of a structure after a failure manifested itself—or for preventive monitoring—to identify anomalies in behavior that may be indicative for impending structural failure.