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Landslides are geomorphological processes that shape the landscapes of all continents, dismantling mountains and contributing sediments to the river networks. Caused by geophysical and meteorological triggers, including intense or prolonged rainfall, seismic shaking, volcanic activity, and rapid snow melting, landslides pose a serious threat to people, property, and the environment in many areas. Given their abundance and relevance, investigators have long experimented with techniques and tools for landslide detection and mapping using primarily aerial and satellite optical imagery interpreted visually, or processed by semi-automatic or automatic procedures or algorithms. Optical (passive) sensors have known limitations due to their inability to capture Earth surface images through the clouds and to work in the absence of daylight. The alternatives are active, "all-weather" and "day-and-night", microwave radar sensors capable of seeing through the clouds and working in presence and absence of daylight. We review the literature on the use of Synthetic Aperture Radar (SAR) imagery to detect and map landslide failures – i.e., the single most significant movement episodes in the history of a landslide – and of landslide failure events – i.e., populations of landslides in areas ranging from a few to several thousand square kilometres caused by a single trigger. We examine 54 articles published in representative journals presenting 147 case studies in 32 nations, in all continents, except Antarctica. Analysis of the geographical location of 70 study areas shows that SAR imagery was used to detect and map landslides in most morphological, geological, seismic, meteorological, climate, and land cover settings. The time history of the case studies reveals the increasing interest of the investigators in the use of SAR imagery for landslide detection and mapping, with less than one article per year from 1995 to 2011, rising to about 5 articles per year between 2012 and 2020, and an average period of about 4.2 years between the launch of a satellite and the publication of an article using imagery taken by the satellite. To detect and map landslides, investigators use a common framework that exploits the phase and the amplitude of the electromagnetic return signal recorded in the SAR images, to measure terrain surface properties and their changes. To discriminate landslides from the surrounding stable terrain, a classification of the ground properties is executed by expert visual (heuristic) interpretation, or through numerical (statistical) modelling approaches. Despite undisputed progress over the last 26 years, challenges remain to be faced for the effective use of SAR imagery for landslide detection and mapping. In the article, we examine the theoretical, research, and operational frameworks for the exploitation of SAR images for landslide detection and mapping, and we provide a perspective for future applications considering the existing and the planned SAR satellite missions. • We examine the theoretic, research, and operational frameworks for landslide failures mapping using SAR images. • SAR imagery is suited to map populations of landslides of different types and sizes in different physiographic settings. • Satellite SAR images can improve landslide rapid mapping, contributing to mitigate landslide risk. • We envisage future applications considering existing and planned SAR satellite missions. [ABSTRACT FROM AUTHOR]