Late Pleistocene and Holocene ground ice are common throughout the Arctic. Some forms of relict ground ice preserve local meteoric water, and their stable oxygen‐ and hydrogen‐isotope ratios can be used to reconstruct past air temperatures. In this paper, we review the formation and sampling of two forms of relict ground ice—wedge ice and pore ice—and recent (2010–2019) advances in paleoclimatological studies of ground‐ice stable isotope records in the Arctic. Recent advances are attributed to better chronological constraints and refined understandings of the systematics and seasonality of relict wedge ice and pore ice. A rich network of ice‐wedge records has emerged, primarily from the Siberian Arctic, whereas pore‐ice records are less common. The ice‐wedge network depicts a robust pattern of late Pleistocene cooling, and remarkably similar temperature depressions during Marine Isotope Stages 3 and 2. Very high‐resolution wedge‐ and pore‐ice stable isotope chronologies have been established recently and used to reconstruct winter and summer climate histories and to assess seasonal dependencies in insolation‐forced climate. Reports of ancient (>125 ka BP) ground ice demonstrate its long‐term persistence, and its potential to expand our knowledge of Quaternary climate dynamics in the terrestrial Arctic.