Full-waveform inversion (FWI) has become an enabling tool for 3D velocity-model building, especially in the shallow part of the seismic image that is well probed by diving waves. Given that FWI provides direct access to P-wave velocities, its application to time-lapse (4D) studies is of obvious interest. Can 4D FWI give fast access to small reservoir production-related velocity changes and compete with traditional 4D time-shift results based on fully processed and imaged reflection data? Also, what algorithmic developments may be needed to achieve robust 4D FWI results? Time-lapse data sets acquired with highly repeatable permanent-reservoir-monitoring (PRM) acquisition systems, such as the one deployed over the Grane Field in the Norwegian North Sea, are well suited to help address these questions. We demonstrate the success of the 4D FWI technique using a synthetic study involving 3D elastic modeling through a highly realistic earth model akin to the actual Grane PRM data. This study indicates there is minimal sensitivity of the method to various residual uncertainties in the data and in the modeling for this acquisition configuration. The 4D FWI results using real time-lapse Grane PRM data acquired in the field with a six-month acquisition interval between vintages show changes at the reservoir level that correlate with both injecting and producing wells. We also find good agreement when comparing the velocity differences from 4D FWI to 4D time shifts and time strains from the fully processed and imaged seismic reflection data. Given that the FWI updates are driven mainly by diving waves, whereas the time-strain analysis uses reflection data, this gives increased confidence in both sets of results. Overall, this case study demonstrates the potential of FWI as a reservoir-monitoring tool.