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Measurements of present‐day surface deformation are essential for the assessment of long‐term seismic hazard. The European Space Agency's Sentinel‐1 satellites enable global, high‐resolution observation of crustal motion from Interferometric Synthetic Aperture Radar (InSAR). We have developed automated InSAR processing systems that exploit the first ~5 years of Sentinel‐1 data to measure surface motions for the ~800,000‐km2 Anatolian region. Our new 3‐D velocity and strain rate fields illuminate deformation patterns dominated by westward motion of Anatolia relative to Eurasia, localized strain accumulation along the North and East Anatolian Faults, and rapid vertical signals associated with anthropogenic activities and to a lesser extent extension across the grabens of western Anatolia. We show that automatically processed Sentinel‐1 InSAR data can characterize details of the velocity and strain rate fields with high resolution and accuracy over large regions. These results are important for assessing the relationship between strain accumulation and release in earthquakes. Plain Language Summary: Satellite‐based measurements of small rates of motion of the Earth's surface made at high spatial resolutions and over large areas are important for many geophysical applications including improving earthquake hazard models. We take advantage of recent advances in geodetic techniques in order to measure surface velocities and tectonic strain accumulation across the Anatolia region, including the highly seismogenic and often deadly North Anatolian Fault. We show that by combining Sentinel‐1 Interferometric Synthetic Aperture Radar (InSAR) data with Global Navigation Satellite System (GNSS) measurements we can enhance our view of surface deformation associated with active tectonics, the earthquake cycle, and anthropogenic processes. Key Points: We produce high‐resolution horizontal and vertical velocity and strain rate fields for Anatolia from Sentinel‐1 InSAR and GNSS observationsVelocity gradients indicate shear strain accumulation along the North and East Anatolian Faults and extension across western AnatoliaInSAR data are critical for capturing high‐resolution details of the velocity and strain rate fields [ABSTRACT FROM AUTHOR]