The Nuclear Emergency Search Team (NEST) is an organization operating under the United States' Department of Energy's National Nuclear Security Administration. Their task is "to be prepared to respond immediately to any type of radiological accident or incident anywhere in the world," primarily terrorist nuclear threats.
In Call of Duty 4: Modern Warfare and Call of Duty: Modern Warfare Remastered, NEST teams are on stand-by following rumors of a nuclear device in the capital city of the small Middle Eastern country. After SEAL Team Six discovers the device, a Russian Warhead provided by Imran Zakhaev and the Ultranationalists, they were called to the scene. They were attempting to disarm it when the device detonated. Because of this, it can be reasonably assumed that the NEST teams did not survive the ensuing explosion.