A couple of excerpts from some awesome articles published on Wikipedia.
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Bounding overwatch
Bounding overwatch, also known as leapfrogging or simply bounding, is the military tactic of alternating movement of coordinated units to allow, if necessary, suppressive fire in support of offensive forward movement or defensive disengagement.
As members of a unit (element to platoon level) take an overwatch posture, other members advance to cover; these two groups continually switch roles as they close with the enemy. This process may be done by "leapfrogging" by fireteams, but is usually done within fireteams along a squad/platoon battle line to simulate an overwhelming movement towards the enemy and make it more difficult for the enemy to distinguish specific targets.
This military tactic takes continuous training and focused coordination to be effectively practiced on the modern battlefield. It was first developed in World War II, when suppressing fire became possible — in other words, when man-portable automatic weapons began to come into general issue.
Example: A squad (2 fireteams) in an urban combat zone must advance to a building 100 feet away, crossing an intersection they believe might be in enemy rifle sights from elevated buildings. If the team simply made a run-for-it, they expose themselves to potential enemy fire without protection.
This is where bounding overwatch comes into play.
One fireteam takes an overwatch position while the other team bounds (a bound is a 3-5 second rush) to a new covered position. This way there is always an overwatch team that can react instantaneously to enemy fire (the bounding team would have to stop, take cover, locate the enemy, and aim before they could return fire). Once the covered position is reached by the bounding team, they now assume overwatch positions while the other team then becomes the bounding team.
By using Bounding Overwatch, this unit is able to effectively move through a hostile urban street and intersection, without unnecessarily exposing themselves to enemy fire.
If enemy contact is made, the overwatch team opens fire and the unit takes up a process called Fire and Maneuver which is very similar to Bounding Overwatch in that teams alternate firing and maneuvering. During fire and maneuver, the commander takes more direct control of team movements and positions.
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Fire and Maneuver
Fire and Maneuver can be performed by units of whatever size appropriate: by as few as two soldiers up to companies or larger. It works when a military unit suppresses the enemy with an appropriate level of fire, while at the same time, another military unit advances. After a short time, the advancing unit will halt and begin suppressing, allowing the previously suppressing unit to advance to a new position and begin the cycle again. Enemy suppression can also be achieved with direct and/or indirect fire from combat support units. Artillery, mortars and armor are a few examples of combat support units often used in fire and movement.
In the United States Military, a basic fire and movement tactic is called overwatch. There also exists several variations of overwatch, generally adding further description to more accurately describe the specific maneuver.
A unit fires upon an enemy to distract or suppress them allowing another unit to assault, flank or encircle the enemy. The enemy will be pinned down and can not react, and will be forced to take cover until the flanking unit engages them.
Suppression
Heavy and continuous suppression fire keeps an opponent suppressed and therefore limits the overall firepower of a unit (if a platoon has 30 soldiers, but only 15 are shooting back because the other 15 are being suppressed, that unit's firepower has been reduced by 50%). The fire cuts down on an enemy's intelligence in that they are not able to assess the situation clearly.
Advance
While a base of fire is set up, the second unit will advance to cover in front, in the process setting up a new base of fire at this point. After a new base of fire has been set up, the first unit will advance, under cover of the new fire base, to a new position and set up another base of fire.
Assault
These actions are repeated until the units have closed upon the enemy position. At this point a unit will close in on the enemy and destroy them, often by throwing grenades, close-quarters battle techniques, and hand-to-hand combat.
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Suppressive Fire
In military science, suppressive fire is a fire that degrades the performance of a target below the level needed to fulfill its mission. Suppression is usually only effective for the duration of the fire. Suppressive fire is not always a direct form of fire towards targets; it can be an effective visual and audible distraction. It is one of three types of fire support, which is defined by NATO as “the application of fire, coordinated with the manoeuvre of forces, to destroy, neutralize or suppress the enemy.”
Before NATO defined the term, the British and Commonwealth armies generally used “neutralisation” with the same definition as suppression. NATO now defines neutralization as “fire delivered to render a target temporarily ineffective or unusable.”
Usage
The purpose of suppression is to stop or prevent a target from observing, shooting or moving. This is useful for tactical reasons, as a suppressed target will be unable to return fire upon vulnerable forces that are moving without cover. This enables forces to advance to new positions that offer more tactical advantages (e.g., a high point). For example, a US Marines article notes that "communication and suppressive fire are what enables movement on the battlefield, giving Marines the upper hand." Suppressive fire may be used to enable a helicopter or boat to land or extract soldiers from a battle zone (the latter is called a "hot extraction").
The primary intended effect of suppressive fire is psychological. Rather than directly trying to kill enemy soldiers, it makes the enemy soldiers feel unable to safely perform any actions other than seeking cover. Colloquially, this goal is expressed as "it makes them keep their heads down" or "it keeps them pinned down". However, depending on factors including the type of ammunition and the target's protection, suppressive fire may cause casualties and/or damage to enemy equipment.
Heavy and continuous fire keeps an opponent suppressed and therefore limits the overall firepower of the enemy unit. Suppressive fire also makes it harder for the enemy to be able to assess the situation clearly.
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