Climate change and nuclear war are currently the most dangerous challenges to human civilisation and survival. The effects of climate change are now sufficient to persuade many governments to take effective measures to reduce greenhouse gas emissions. Today there are about 27,000 nuclear warheads, many at least ten times more powerful than the Hiroshima and Nagasaki bombs, and a meaningful medical response to a nuclear attack is impossible. Nevertheless, the threat of nuclear war does not raise public concern, and indeed the nuclear-weapon states are upgrading their capability. The only effective preventive measure is the abolition of nuclear weapons. Steps towards this include: a Fissile Material Cut-off Treaty, for the nuclear weapon states to observe their obligations under the Nuclear Non-Proliferation Treaty, and for the Comprehensive Test Ban Treaty to enter into force. The ultimate need is for a Nuclear Weapons Convention; International Physicians for the Prevention of Nuclear War have launched an International Campaign to Abolish Nuclear weapons (ICAN) to promote a NWC.