Open bolt

A fully automatic firearm is said to fire from an open bolt if, when ready to fire, the bolt and working parts are held to the rear of the receiver, with no round in the chamber. When the trigger is actuated, the bolt travels forward, feeds a cartridge from the magazine or belt into the chamber, and fires that cartridge in the same movement. Like any other self-loading design, the action is cycled by the energy released from the propellant, which sends the bolt back to the rear, compressing the mainspring in readiness for firing the next round. In an open-bolt gun firing semi-automatically, the bolt is caught and held at this point by the sear after each shot; and in automatic open-bolt fire, it's caught and held in this manner whenever the trigger is released. In contrast to this, in closed-bolt guns the trigger and sear doesn't affect the movement of the bolt directly.
Generally, an open-bolt firing cycle is used for fully automatic weapons and not for semi-automatic weapons (except some semi-automatic conversions of automatic designs). Firearms using advanced primer ignition blowback inherently fire from open bolt only.
Advantages.
Compared to a closed-bolt design, open-bolt weapons generally have fewer moving parts. The firing pin is often part of the bolt, saving on manufacturing costs; the inertia of the bolt closing also causes the fixed firing pin to strike a blow on the primer, without need for a separate hammer/striker and spring. In automatic weapons an open bolt helps eliminate the dangerous phenomenon known as "cook-off", wherein the firing chamber becomes so hot that rounds spontaneously fire without trigger input, continuing to cycle until the ammunition is exhausted. Open-bolt designs typically remain much cooler in operation than closed-bolt types due to the airflow allowed into the chamber, action and barrel during pauses between bursts; moreover, unlike in the case of the closed-bolt format, the initial round in a burst is not introduced into the chamber until the moment before firing, and is thus only exposed to the residual heat for a fraction of a second. These two features combine to make open-bolt operation more suitable for weapons such as machine guns, which are intended to be capable of prolonged automatic fire.
Disadvantages.
Some open-bolt designs can suffer from a condition in which bolt retention fails and the weapon will discharge with no trigger input, with potentially disastrous consequences. In addition to this, simple submachine guns such as the Sten, even when uncocked, can fire spontaneously when dropped onto a hard surface, as the collision can jolt the bolt backward far enough that on returning it will pick up a round from the magazine, chamber it and fire it; the risk is intrinsic to hand-held open-bolt guns unless safety features are included in the design.
Another shortcoming of the open-bolt principle is that there is a brief delay between the trigger-pull and the firing of the cartridge because the bolt has to move forward a significant distance between the two events. This initial delay can be an obstacle to accuracy, especially when attempting to shoot a moving target, or when shooting in motion. The problem is generally less of a concern in full automatic fire since after the first shot, the operation is effectively indistinguishable from that of a firearm that fires from a closed bolt; but is a more significant shortcoming when using such weapons in semi-automatic mode; or when such guns are converted to semi-automatic operation for legal reasons.
In aerial combat, during the years of piston-engined warplanes open-bolt machine guns and autocannon presented problems as forward-firing aerial weapons in fighters (at least on the usual tractor configuration single-engine aircraft). The reason being that, as discussed above, detonation of the cartridge primer in these guns was a function of the movement of the whole bolt rather than an independently-acting firing pin. This in conjunction with the initial delay between the initial trigger-pull and the firing of the first round makes the moment when this and each subsequent cartridge in a burst is fired significantly less predictable or controllable, to the extent that whereas closed-bolt machine guns could be synchronized to fire through the arc of the propeller blades, open-bolt designs could not do so without extensive modification. It should also be noted that, as aerial combat characteristically involves shooting at extremely fast-moving targets and often from an extremely fast-moving position the intrinsic firing delay of open-bolt guns is particularly undesirable, even for the automatic weapons ubiquitous in this form of warfare. 
In guns that use an unlocked, simple blowback action, calibers over 9×19mm Parabellum become increasingly less practical, particularly as hand-held weapons, because of the need for correspondingly heavier bolts as the chamber pressure increases. In simple blowback open-bolt designs, even in such relatively low-power calibers, accuracy can suffer somewhat due to the potential disruption of aim caused by the violent movement of the heavy bolt mass within the gun. This can be problematic in two separate ways: in automatic fire the continual movement of such a bolt may make it difficult to keep the gun on target during fire; while in semi-automatic fire or at the beginning of each automatic burst the initial delay problem just described above is exacerbated, as controlling the gun during this brief interval is particularly difficult where the bolt-movement is particularly violent. However while this characteristic delay is innate to the open-bolt format, a lighter bolt can be used in more sophisticated delayed-blowback open-bolt designs, thus reducing the gap in accuracy performance between open and closed bolt types. The significance of the heavy bolt problem is not that it cannot be solved, but that it remains a current issue because most submachine guns use simple blowback for reasons of economy and simplicity.
Another problem is that, since the weapon must be carried with the bolt open in order to fire promptly, this leaves the breech and action internals open to dirt and dust contamination through the open ejection port, unless some sort of cover can be devised. Some versions of the open-bolt M3 submachine gun utilized a hinged sheet metal ejection port cover that doubled as a safety; when closed, it both covered the ejection port and blocked the bolt from closing. When ready to fire, the user simply flipped the cover down, opening the ejection port and unblocking the bolt.
Other characteristics.
An open-bolt weapon will typically have a higher rate of automatic fire than a comparable closed-bolt weapon as the bolt simply needs to return forwards in order for the weapon to fire again, while a closed-bolt design has the additional step of the hammer striking the firing pin. Having a higher fire rate can be both an advantage and disadvantage depending on the situation. For handheld weapons, typically a lower rate of fire is desirable, as this will conserve ammunition and help keep the level of recoil more manageable. For vehicle-mounted weapons or fixed emplacements, however, a higher rate of fire is often desirable. In these situations, ammunition and recoil are less of a concern and the higher rate of fire will increase the likelihood of a round hitting the target, particularly when employed against fast-moving targets such as aircraft.
Many movies and video games portray open-bolt weapons as needing to be cycled after reloading. This is not generally true, however, as open-bolt weapons send the bolt carrier back into a cocked position via the excess gas after the last round is fired. The exception to this is if the weapon is fully automatic and the trigger is held down after the last round was fired (and the gun does not have a "last round bolt hold open" mechanism) at which point the bolt will fly forward once more and stay there. In this case, the bolt merely needs to be retracted to the rearward position and does not return forward as is sometimes portrayed.
Another feature of open-bolt designs is that the magazine simply needs to be removed to completely unload the weapon. A closed bolt requires the second step of cycling the action to remove the last round in the chamber (unless the weapon features an automatic hold-open device). It is essential to remove a loaded magazine before performing maintenance, or trying to cycle or close the bolt (as is often done to keep the weapon clean when not in use). If one were to close the bolt (say by pulling the trigger and riding the bolt to the closed position), as soon as the bolt closes it will fire if a loaded magazine was left in the gun. This may be true with weapons utilizing a striker, but not with a weapon using a fixed firing pin, which relies on the momentum of the bolt to impart the energy to ignite the primer. This is a common feature in basic submachine guns like the Sten gun or M3 "Grease Gun", and even some machine guns. With a fixed firing pin, when the bolt is closed gently, without the momentum of the bolt closing at normal speed, there is not enough force imparted to the firing pin to ignite the primer. In this circumstance there will be a round in the chamber and a firing pin pressing on it with some force, but not enough to ignite the primer, which requires a sharp, focused impact. However, the weapon would be at risk of firing if dropped, much like the danger of loading spitzer bullets into a weapon with a tube magazine. A related issue is that the safety of an open-bolt weapon must be designed to lock the bolt in the rearward position. Often safeties only block the movement of the trigger, so, as explained above, if the weapon is dropped or if the sear becomes worn, the bolt can slam home, firing the weapon (although this issue is true to a degree in closed-bolt firearms as well).
Uses.
Closed-bolt designs are often used in rifles. The improved accuracy of closed-bolt weapons is more desirable, while the poorer heat dissipation is less of an issue for slower-firing weapons. In contrast, open-bolt designs are more often used in automatic weapons, such as machine guns. For fast-firing automatic weapons, heat will rapidly build up from sustained firing, but accuracy is of less importance. Thus, the improved heat dissipation of open-bolt designs is generally more desirable in automatic weapons. Due to submachine guns having somewhat of an intermediate role between accurate rifles and rapid-fire machine guns, different SMGs have been designed with both closed (H&K MP5 series, B&T MP9, CZ Skorpion) and open bolts (Thompson submachine gun, MAC-10, Uzi).
Legality.
Under United States federal law, fully automatic firearms are restricted under the National Firearms Act and other laws. In 1982, the Bureau of Alcohol, Tobacco, Firearms and Explosives ruled that semi-automatic open-bolt firearms manufactured after the date of the ruling are to be treated as fully automatic as they may be "readily converted" to fully automatic fire. However, any prior made semi-automatic open bolt was grandfathered in and is treated like any non-NFA firearm. The open bolt semi-automatic versions of certain guns are often as costly as their fully automatic counterparts. This is because prior to the Hughes Amendment in 1986 most semi-automatic open bolt Mac-10s, Mac-11s and several other models were lawfully converted to full auto making these rare semi-automatic open bolts even more rare and desirable as collector items.