Large-scale ground deformation in Iceland is dominated by extensional plate-boundary deformation, where the Mid-Atlantic Ridge crosses the island, and by uplift due to glacial isostatic adjustment from thinning and retreat of glaciers. While this deformation is mostly steady over multiple years, it is modulated by smaller-scale transient deformation associated with e.g., earthquakes, volcanic unrest, and geothermal exploitation. Here we combine countrywide Sentinel-1 interferometric synthetic aperture radar (InSAR) data (from six tracks) from 2015 to 2021 with continuous GPS observations to produce time-series of displacements across Iceland. The InSAR results were improved in a two-step tropospheric mitigation procedure, using (1) global atmospheric models to reduce long-wavelength and topography-correlated tropospheric signals, and (2) modeling of the stochastic properties of the residual troposphere. Our results significantly improve upon earlier country-wide InSAR results, which were based on InSAR stacking, as we use more data, better data weighting, and advanced InSAR corrections to produce time-series of ground displacements instead of just velocities. We fuse the three ascending and three descending track results to estimate maps of near-East and vertical velocities, which clearly show the large-scale extension and GIA deformation. Using a revised plate-spreading and glacial isostatic adjustment models, based on these new ground velocity maps, we remove the large-scale and steady deformation from the InSAR time-series and analyze the remaining transient deformations. Our results demonstrate the importance of (1) mitigating InSAR tropospheric signals over Iceland and of (2) solving for time-series of deformation, not just velocities, as multiple transient deformation processes are present.