On Stardate 48315.6 the USS Voyager was transported beyond their control, 70,000 lightyears across the galaxy to the Delta Quadrant. There, without any aid from Starfleet, they began their 70-year journey home. In their numerous encounters they came into contact with many dangerous and violent species. Having a limited crew with no chance of reinforcements, they determined that they needed a specialized team to handle the more dangerous situations. Tuvok, Voyager's Chief of Security, assembled an elite force of security personnel which he named the "Hazard Team".
Voyager's return to Federation space in 2377, and the reports of the Hazard Team's exploits, coincided with an independent Starfleet program being discussed to perform just such tasks. The Borg invasion of 2367 highlighted the need for these highly trained forces, when the prospect of retaking a captured planet became very real. Since then, Starfleet began developing their concept of the Rapid Response team. In the rare times when Starfleet must respond with controlled, overt force - retaking a starbase captured by Cardassian soldiers or rescuing prisoners from Breen pirates, for example - it would call upon the special services of its Rapid Response forces. The effectiveness of Voyager's Hazard Team helped to push the idea from concept to reality.
The members of Starfleet see themselves primarily as explorers and diplomats, and Starfleet prefers to resolve conflicts as quickly and peacefully as possible. There are times, however, when force becomes the only option. Starfleet's Rapid Response forces respond quickly to situations requiring specialized, armed training. They differ from more traditional security officers in that they receive extensive training in personal combat, such as guerilla warfare, demolitions, and weapons training, at the expense of more well-rounded Starfleet training (in the sciences and diplomacy, for example). Although the first to be deployed in a hostile situation, Starfleet's Rapid Response forces remain an option of last resort. It specializes in the traditional arts of assaulting and holding a position (known as point defense), and trains to tackle situations as divergent as storming a well defended position, hostage rescue, reconnaissance, stealthy infiltration, and antiterrorism actions.
Starfleet maintains few of these personnel, because of their lack of utility in other areas. Certain elements at Starfleet Command have proposed expanding the program, and improving the capabilities of these forces, citing Dominion aggression during the war. So far, cooler heads at Starfleet and on the Federation council have prevailed. Starfleet would prefer to allocate personnel and resources to more positive endeavors, like exploration. It currently maintains some 10,500 personnel throughout the Federation, stationed at strategic locations, such as along the Cardassian border and near Gorn space. In times of peace, they occupy their time with training and conventional security activities. In order to make them more "useful," the Chief of Starfleet Security has authorized a program assigning individual members to starships, to serve in the more typical role of security officer.
The Superintendent of Starfleet's Rapid Response teams answers directly to the Chief of Starfleet Security. Contingents are posted at Starbases 82, 221, and 500 among others, typically using Steamrunner- and Saber-class starships for rapid deployment in large numbers. Starfleet outfits these individuals with an armored uniform, a compression phaser rifle, a type-II phaser, and a tricorder. Additional equipment is assigned as needed.
Often, Rapid Response teams are grouped into a Task Group. A Task Group will usually consist of anywhere from three to five "teams." The typical team consists of one Command personnel, one Medical personnel, and two specially trained Security personnel. A team can be expanded if needed by grouping multiple teams. Quite often a Task Group will also include an Engineering specialist, a demolitions specialist, a covert operations specialist, and a science specialist, who can be individually added to a team as needed.
Task Groups are identified by numbers, such as the "32nd Starfleet Rapid Response Task Group." Individual teams are part of Task Groups, even if they are not serving with other teams in their Group. And while the official term for the highly trained personnel is a Starfleet Rapid Response Team, team members usually refer to themselves as a "Hazard Team", in homage to the first of their kind on board Voyager.
Currently, the 48th Starfleet Rapid Response Task Group has been assigned to the USS Atlantis, and is comprised of 13 personnel. Their Personnel dossiers are available here. The 501st Starfleet Rapid Response Task Group has been assigned to the USS Independence-A, and is comprised of 20 personnel.