Independent rear suspension (or IRS) refers to the use of rear suspensions in automobiles in which the right wheel is mostly or entirely decoupled from the left, and vice versa. It is normal (Except in heavy-duty four wheel drive vehicles) to have independent front suspension, but independent rear is a fairly recent development in automotive technology. Independent suspension is used in automobiles to increase traction.
The one drawback of IRS is that decoupling the wheels tends to increase body roll, the tendency for the body to "lean into" a turn. This can be combated by the use of an anti-roll bar, or "sway bar." This is a generally C-shaped piece of metal whose ends connect (usually) to the lower suspension member, and whose back is connected to the chassis in two places using somewhat flexible end links with bushings. It flexes somewhat under load and generally serves to make the two parts of the suspension want to move up and down in unison. This substantially reduces body roll, and is nearly always employed on the front suspension of modern vehicles, and frequently (but less so) on the rear as well.
There are really only four types of independent rear suspension commonly used today, or which have commonly been used; swing axle, torsion beam, trailing arm, and double wishbone. The MacPherson strut suspension has also become more popular as a rear suspension as average vehicle weights have fallen.
Swing axle IRS is characterized by having a single joint or knuckle which pivots, generally right at the differential. This implies that as the suspension member (the axle itself, or an accompanying A-arm) rises and falls, the camber of the wheel changes. This results in inconsistent handling, especially during periods of body roll, as the camber of the two wheels will change inconsistently, as will the distance between the points at which the tires contact the ground. This is the type used on the original Volkswagen Beetle.
Torsion beam suspension essentially consists of a structural sway bar. An axle runs from the hub at each end of the C to a differential in the case of driven torsion beams, but it is most often used in front wheel drive vehicles. They are advantageous as they are lightweight, but the wheel moves forward and back as it rises and falls. Torsion beam suspension is used on a multitude of supercompact cars, and on minivans.
Trailing arm IRS features an arm which hangs from a mount point on the chassis that follows its mount points, meaning it sits behind them. It is usually accompanied by an axle featuring a CV joint in order to handle the problem that as the suspension raises and lowers, the distance from the leftmost point of the axle to the rightmost part of the axle would normally change. Trailing arm suspension is more consistent than swing axle, but still shares its problem, simply to a far lesser degree. (The suspension member is pivoting along a different axis, thus camber change is reduced or eliminated.) Unfortunately, trailing arm suspension is quite heavy. This is the system that was used on most models of Porsche, including the 944 from the late 1970s and early 1980s; It was also used on some Nissans, most especially the 280ZX, and it is common on front wheel drive Volkswagens. A variation of the semi-trailing arm suspension called the "Weissach Axle" was used on the Porsche 928 which has a pivot point incorporated in its design in order to deliberately cause the rear suspension to change toe under hard breaking, which was done to eliminate an oversteer condition.
Double wishbone suspension is by far the best independent suspension available, especially when you lump its descendant, multilink suspension in with it. Double wishbone uses two H-shaped members, one upper and one lower, to maintain constant camber as the wheel changes height. It is also generally accompanied by axles with CV joints for the same reason as semi trailing arm. Double wishbone is very rigid and provides absolute camber control. Multilink suspension provides the same benefits but at a savings in weight and space by using more suspension links than two; often as many as five. It can realistically be considered the same as double wishbone, however, as it uses essentially the same approach (triangulation) to provide complete rigidity and control.
It is worth mentioning the use of MacPherson strut suspension in independent rear suspensions. The MacPherson system has long been used on the front of cars because it takes up the least space of any independent suspension. However, it does not provide excellent control over camber; the benefit over the swing axle is that all camber changes are negative, which is to say that the top of the wheel moves toward the center of the car. This tendency to increase negative camber during periods of squat actually improves handling during cornering in some situations. However, inconstant camber can be a big problem in the rear of a rear wheel drive vehicle as it changes your traction during acceleration considerably. Rear MacPherson suspension was used most notably in the Lancia Delta which was a very successful entry in various rally races, and a modified MacPherson suspension is still used in the rear of most Subaru vehicles.