Command of FEC is led by a Colonel or LTC Virtually all information about the unit is highly classified and details about specific missions or operations generally are not available publicly.

Their first major engagements took place during the Zapatista uprising in the well known "Operación Arcoiris" (Operation Rainbow), where they employed counter insurgency tactics against the EZLN socialist guerrilla group, infiltrating and eliminating enemy targets in the jungle terrain of the southern state of Chiapas.

One of the first times its operators were seen in public was hours after the successful capture of Osiel Cárdenas Guillén as they arrived in Mexico City in 2003, during which they killed some of the elite personal security team of the drug lord; as the top leader of the Gulf Cartel at the time, Osiel was one of the most wanted men in Mexico and the United States They were also responsible for hunting down almost all of the first generation of "Los Zetas”, (ex-GAFEs that deserted from the Mexican army to become security for the Gulf Cartel until they splintered to form their own organization) since they knew how they operated and how to counter them, it is mentioned that they located and then gunned down the first leader and co-founder of Los Zetas, Arturo Guzman Decena in the border city of Matamoros in 2002.

The FER was in charge of the raid that ended up with the assassination of one of the most famous Sinaloa Cartel leaders, Ignacio "Nacho" Coronel, the operation took place in the luxury suburb of Zapopan, Jalisco during the year 2010.

At their funeral, the Mexican High Command, the Secretaries of National Defense and the Navy, as well as the President of Mexico (at the time), Enrique Peña Nieto, could be seen attending the ceremony.

In the same year of 2015, through detailed month surveillance they successfully located and captured the highly violent Los Zetas cartel leader, Omar Treviño Morales, in a luxury neighborhood in San Pedro Garza García, Nuevo León.

On August 2, 2020, José Antonio Yépez Ortiz (El Marro), main leader of the Santa Rosa de Lima Cartel (CSRL), was captured by the FER.