Global Navigation Satellite System data across the New Madrid seismic zone (NMSZ) in the central United States over the period from 2000 through 2014 are analyzed and modeled with several deformation mechanisms including the following: (1) creep on subsurface dislocations, (2) postseismic frictional afterslip and viscoelastic relaxation from the 1811–1812 and 1450 earthquakes in the NMSZ, and (3) regional strain. In agreement with previous studies, a dislocation creeping at about 4 mm/yr between 12 and 20 km depth along the downdip extension of the Reelfoot fault reproduces the observations well. We find that a dynamic model of postseismic frictional afterslip from the 1450 and February 1812 Reelfoot fault events can explain this creep. Kinematic and dynamic models involving the Cottonwood Grove fault provide minimal predictive power. This is likely due to the smaller size of the December 1811 event on the Cottonwood Grove fault and a distribution of stations better suited to constrain localized strain across the Reelfoot fault. Regional compressive strain across the NMSZ is found to be less than 3 × 10−9/yr. If much of the present-day surface deformation results from afterslip, it is likely that many of the earthquakes we see today in the NMSZ are aftershocks from the 1811–1812 New Madrid earthquakes. Despite this conclusion, our results are consistent with observations and models of intraplate earthquake clustering. Given this and the recent paleoseismic history of the region, we suggest that seismic hazard is likely to remain significant.