Many arid grasslands around the world are affected by woody plant encroachment and by the replacement of a relatively continuous grass cover with shrub patches bordered by bare soil. This shift in plant community composition is often abrupt in space and time, suggesting that it is likely sustained by positive feedbacks between vegetation and environmental conditions (e.g. resource availability) or disturbance regime (e.g. fire or freeze). These feedbacks amplify the effects of drivers of shrub encroachment, i.e. of conditions favouring a shift from grass to shrub dominance (e.g. overgrazing, climate change). Here, we review some major drivers and feedbacks and identify the basic stages in the transition from grassland to shrubland. We discuss some possible scenarios of interactions between drivers and feedbacks that could explain the transition from a stage to the next and the potential irreversibility of the shift from grass to shrub dominance. We introduce a simplistic modelling framework that can integrate the various drivers to explain the emergence of bistability for shrub-encroached grassland systems. Published 2011. This article is a U.S. Government work and is in the public domain in the USA.