A review of recent progress in understanding the dynamics, internal structure and palaeoenvironmental potential of ice wedges and sand wedges is presented, based on literature published between 2008 and 2015. Ice wedges constitute the most ice‐rich and widespread periglacial landform in permafrost lowlands. Thus, progress in understanding the processes associated with them, using a large variety of direct and indirect field and remote sensing methods, is important, particularly in a changing climate with increased potential for ice‐wedge degradation. Ice‐wedge polygons have been found to control microclimate, hydrology and greenhouse gas fluxes from permafrost. New technologies have allowed the identification of more fossil polygons, increasing their role in reconstructing periglacial conditions. Study of ice‐wedge casts, sand wedges and ice wedges has improved palaeoenvironmental reconstruction, particularly from the last glacial period and the Holocene, of changes to these landforms in both present and former permafrost areas. Polygons on Mars have recently attracted considerable attention, primarily due to increased remote sensing capabilities and even on‐site investigations, which identify ice in these landforms. Copyright © 2016 John Wiley & Sons, Ltd.