Periods of exceptional climate change in Earth history are associated with a dynamic response from the geosphere, involving enhanced levels of potentially hazardous geological and geomorphological activity. The response is expressed through the adjustment, modulation or triggering of a broad range of surface and crustal phenomena, including volcanic and seismic activity, submarine and subaerial landslides, tsunamis and landslide 'splash' waves, glacial outburst and rock-dam failure floods, debris flows and gas-hydrate destabilization. In relation to anthropogenic climate change, modelling studies and projection of current trends point towards increased risk in relation to a spectrum of geological and geomorphological hazards in a warmer world, while observations suggest that the ongoing rise in global average temperatures may already be eliciting a hazardous response from the geosphere. Here, the potential influences of anthropogenic warming are reviewed in relation to an array of geological and geomorphological hazards across a range of environmental settings. A programme of focused research is advocated in order to: (i) understand better those mechanisms by which contemporary climate change may drive hazardous geological and geomorphological activity; (ii) delineate those parts of the world that are most susceptible; and (iii) provide a more robust appreciation of potential impacts for society and infrastructure.