Erosion is the removal of material caused by the eroding power of a flow, though neglecting physico-chemical effects. Soil erosion occurs in various situations in the fields of hydraulics and geomechanics: sediment transport in rivers and open channel flows subjected to free surface flows, pipe flow with erosion, sink-hole, fluidization, backward erosion, seepage erosion, sand production, contact erosion, internal erosion and suffusion. Naturally, this list is not exhaustive. There is a large body of literature on modelling soil erosion in the field of sediment transport and the hydraulics of free-surface flows. However, most of these studies have taken a global approach to the subject. Erosion is regarded as a gradient of transport capacity at equilibrium, rather than a dynamic process of particle removal caused by the flow, and the question of fluid/grain behaviour has been given relatively little attention. In recent years, researchers and the geomechanics community have displayed increasing interest in understanding soil erosion. Much effort has been carried out by the European Group, ICOLD (International Committee on Large Dams), has dedicated considerable effort to better understand the physical processes and mechanics of internal erosion. This group is involved in the preparation of the document Assessment of the risk of internal erosion of water retaining structures: dams, dykes and levees, scheduled for release in 2012. This is the first ICOLD Bulletin devoted to internal erosion! ALERT Geomaterials - The Alliance of Laboratories in Europe for Research and Technology (http://alert.epfl.ch) - is an international network, grouping 25 Universities or Organisations, that are highly active in the numerical modelling of geomaterials and geostructures. The subject of sand production was addressed in the 2006 ALERT Graduate School, focusing on petroleum related geomechanics. A full session of the 2009 ALERT Workshop was devoted to erosion in geomaterials. The topics addressed covered some of the problems liable to occur in natural soils and in the soils of hydraulic works (dykes, levees, earth dams). This special issue is a continuation of the 2009 ALERT Workshop session. Emphasis is given here to recent and innovative results not presented to the workshop. Notably, three processes are investigated: the backward erosion piping process (van Beek et al., Sellmeijer et al.), the internal erosion and suffusion process (Salehi Sadaghiani and Witt, Bonelli and Marot, Golay and Bonelli), and the impinging jet with erosion process (Regazzoni and Marot). Testing is addressed in three papers (van Beek et al., Salehi Sadaghiani and Witt, Regazzoni and Marot), whereas modelling is considered in four papers (Sellmeijer et al., Cottereau and Díez, Bonelli and Marot, Golay and Bonelli). The instabilities that result from erosion in geomaterials gives rise to a wide range of hazards. Understanding these processes implies efforts that must be sustained by the geomechanics community, in the challenging field of erosion in geomechanics in general, and in fluid-grain interaction in particular. We believe that this volume provides a valuable basis for further progress in this direction for students, researchers and practitioners.