I mages of surface displacements in response to tectonic forces can provide independent, spatially dense observations that assist in understanding sub-surface processes. When considered independently or augmented with more traditional observations of active tectonics such as seismicity and ground mapping, these measurements provide constraints o n spatially and temporally variable fault behavior across the seismic cycle. Models of fault behavior inferred from these observations in turn allow us to address topics in geologic hazards assessment, the long- a nd short - term character of strain in defor ming regions, and the interactions between faults throughout the crust. In this dissertation, I use remotely sensed observations of ground displacements from interferometric synthetic aperture radar (InSAR) t o approach several problems related to earthquak e and aseismic fault slip. I establish image p rocessing and inverse methods for better detailing subsurface fault slip and apply these to the 2 010 - 2011 Canterbury, New Zealand sequence. Then, I focus on the active tectonics of the Zagros Mountains in south ern Iran. There, I show through orogen -wide InSAR time series analysis that active strain is accommodated across the width of the mountain belt. I also use a combination of InSAR, local seismicity, and structural modeling to demonstrate that strain is v ert ically partitioned within the Zagros fold-and - thrust belt, with earthquakes controlling deformation in the underlying basement while the overlying sedimentary section shortens in t ransient, earthquake- triggered aseismic slip events. In certain examples, th ese aseismic slip events directly contribute to the growth of fault -bend folds. I use these inferences to explore a p reviously noted discrepancy between observed shortening and that which is expected from k nown earthquakes. I show that the earthquakes and short - term aseismic slip cannot account f or this discrepancy, and that additional deformation mechanisms must be active.