Striking developments in the climate system in recent years have reinforced the view that anthropogenic global warming is unlikely to cause a smooth transition into the future. The record minimum area coverage of Arctic sea-ice in September 2007 drew widespread attention, as has the accelerating loss of water from the Greenland and West Antarctic ice sheets (Chapter 3). These large-scale components of the Earth System are among those that have been identified as potential ‘tipping elements’ – climate sub-systems that could exhibit a ‘tipping point’ where a small change in forcing (in particular, global temperature change) causes a qualitative change in their future state (Lenton et al., 2008). The resulting transition may be either abrupt or irreversible, or in the worst cases, both. The most ‘policy-relevant’ tipping elements have been defined as those that (i) have a tipping point that could be crossed this century, (ii) would undergo, as a consequence, a qualitative change within this millennium, thereby (iii) affecting (if not damaging) a large number of people. For a full definition of a tipping element and its tipping point, see Box 7.1 (and Lenton et al., 2008). In IPCC terms such changes are referred to as ‘large-scale discontinuities’ (Smith et al., 2009). Should they occur, they would surely qualify as dangerous climate changes (Schellnhuber et al., 2006) (although not all are equally dangerous, as we will explore further).