Nuclear terrorism is a real and urgent threat. Given the potentially catastrophic consequences, even a small probability of terrorists getting and detonating a nuclear bomb is enough to justify urgent action to reduce the risk. Al-Qaeda and North Caucasus terrorist groups have both made statements indicating that they seek nuclear weapons and have attempted to acquire them; these groups are presented together as a case study to assess nuclear terrorism as a present and future threat. (The only other terrorist group known to have systematically sought to get nuclear weapons was the Japanese cult group Aum Shinrikyo.) This study makes the case that it is plausible that a technically sophisticated group could make, deliver, and detonate a crude nuclear bomb if it could obtain sufficient fissile material. The study offers recommendations for actions to reduce this danger.