In recent decades, Greenland's peripheral glaciers have experienced large-scale mass loss, resulting in a substantial contribution to sea level rise. While their total area of Greenland ice cover is relatively small (4%), their mass loss is disproportionally large compared to the Greenland ice sheet. Satellite altimetry from Ice, Cloud, and land Elevation Satellite (ICESat) and ICESat-2 shows that mass loss from Greenland's peripheral glaciers increased from 27.2 +/- 6.2 Gt/yr (February 2003-October 2009) to 42.3 +/- 6.2 Gt/yr (October 2018-December 2021). These relatively small glaciers now constitute 11 +/- 2% of Greenland's ice loss and contribute to global sea level rise. In the period October 2018-December 2021, mass loss increased by a factor of four for peripheral glaciers in North Greenland. While peripheral glacier mass loss is widespread, we also observe a complex regional pattern where increases in precipitation at high altitudes have partially counteracted increases in melt at low altitude.