We review new advances in volcano-ice interactions on Mars and focus additional attention on (1) recent analyses of the mechanisms of penetration of the cryosphere by dikes and sills; (2) documentation of the glacial origin of huge fan-shaped deposits on the northwest margins of the Tharis Montes and evidence for abundant volcano-ice interactions during the later Amazonian period of volcanic edifice construction and (3) the circumpolar Hesperian-aged Dorsa Argentea Formation, interpreted as an ice sheet and displaying marginal features (channels, lakes and eskers) indicative of significant melting and interior features interpreted to be due to volcano-ice interactions (e.g. subglacial volcanic edifices, pits, basins, channels and eskers). In this context, we describe and analyse several stages and types of volcano-ice interactions: (1) magmatic interactions with ice-rich parts of the cryosphere; (2) subglacial volcanism represented by intrusion under and into the ice and formation of dikes and moberg-like ridges, intrusion of sills at the glacier-volcano substrate interface and their evolution into subglacial lava flows, formation of subglacial edifices, marginal melting and channels; (3) synglacial (ice contact) volcanism represented by flows banking up against glacier margins, chilling and forming remnant ridges and (4) post-glacial volcanism and interactions with ice deposits.