In car-crafting lore, there are anywhere from one to three sealed boxes in any performance machine. One is the torque converter, another is the computer that does its electronic thing, and the third is the universal unknown--the shock absorber. In fact, even its name is not technically correct. Absorbing the "shock" of bumps and suspension loading is actually performed by the springs in the suspension. Controlling the energy stored in the spring is the shock's real job, and everywhere else except in the U.S. it's called a spring damper.
Basics
Especially with an enigmatic thing like a shock absorber, we need to start with the basics. First, it's critical to emphasize that shocks do not support the weight of a vehicle, and they better not be propping up one or more corners of your car. If this is the case, you have serious problems. The exception to this is the air shock, which was popular about 30 years ago but was never a good idea. We also need to go over a couple of terms often used in discussing shock absorbers. As the shock is pushed together, this is called bump or compression. As the shock expands, this is called rebound. When the vehicle encounters a bump and compresses a spring, energy is stored in the spring. As the spring expands against the weight of the sprung mass of the vehicle, the shock absorber forces oil through various metered orifices in the shock valving to control this action.
Shock absorbers are basically hydraulic units that are inherently velocity sensitive. That means that as the suspension is compressed at a faster rate, the chassis needs a device that can apply progressively more force to dampen the additional spring energy as it expands in rebound. Nonadjustable shock absorbers are created with a certain bump and rebound rate as defined by the manufacturer to create a given suspension control and a comfortable ride all in one package. But when we get into high-performance automobiles, this compromise is usually less than ideal. This is especially important with specialized applications like drag racing or road-course racing that demand specific bump and rebound curves in order for the shock absorbers to work best.
Struts are a combination of a suspension component and shock absorber. You'll find struts on the front suspension on cars like '79 to '93 Fox-body Mustangs and third-generation Camaros.
Characteristics
If you've ever driven a car with dead shocks, then you've lived the definition of "mushy". Without that application of dampening force, the springs will virtually never stop oscillating. This loss of control has been best described as four independent pogo sticks on the four corners of the car all bouncing at a different rate. As the spring oscillates, it also unloads the tires, and it doesn't take much of an imagination to see that if you cannot control the contact patch between the tires and the road, you have no chance of controlling the car in any type of dynamic situation.
Another important aspect of shock design is that they always offer more dampening control in rebound than in bump, since the shock needs this additional rebound force to control the spring as it expands. This relationship can and does change with each manufacturer's shocks and the specific tuning for a given vehicle. But since car crafters are always asking their cars to do different things, a given shock absorber valving might not be correct or even close for all different kinds of cars. This requirement spawned a huge market for adjustable shock absorbers that could be given a wide range of bump and rebound control.
Shock Design
Performance shock absorbers are offered in both single- and double-adjustable configurations. Double-adjustable shocks offer the ability to trim the bump and the rebound separately, but you pay for that with a much higher cost. Single-adjustable shocks allow changes to the rebound portion of the shock. These shocks are more expensive than nonadjustable shocks but far less expensive than double-adjustables. Examples of single-adjustable shocks are the Koni, Tokico, Competition Engineering, and QA1 dampers.
Among both adjustable and nonadjustable shocks, there are basically two different designs: the mono-tube and twin-tube. The twin-tubes are also the standard low-pressure hydraulic dampers. Mono-tube shocks employ high-pressure gas as an additional effort to minimize the creation of bubbles in the hydraulic oil that occur any time oil is pushed through an orifice. Using high-pressure nitrogen gas in a sealed container, like a bag, limits the creation of bubbles in the oil. This helps shock performance especially in handling situations where they are subjected to serious abuse. The twin-tube, low-pressure shocks still work well, but generally the high-pressure shocks offer a slight advantage. Koni for example, sells both styles of shocks, as does Tokico and Edelbrock. This gives you a choice in terms of performance versus price.
The sole reason for shock absorbers is to maintain vehicle stability in both cornering and acceleration. Controlling the spring during rebound after a bump maintains tire contact with the pavement. When the shock absorber is properly matched to the chassis combination, the tire maintains optimal contact with the road, corners better, and is much more responsive to driver input. | 
Most shocks absorbers look alike, so you really need to know more about them in order to employ them properly. For example, these Koni front shocks for an early Chevelle or Camaro offer a rebound adjustment feature, but they must be removed from the vehicle and compressed fully to adjust. |
In graph form, shock absorbers plot force (on the vertical axis) versus speed of shock-piston movement in the shock body (on the horizontal scale). In this graph, rebound force is in the upper portion, while bump is in the lower portion of the graph. The dotted line represents a stock shock, while the solid line represents a firmer rebound and compression force. Adjustable shocks would offer several lines of greater force based on the adjustment from full soft to full hard. | 
Stock-type shocks do an adequate job of controlling pitch and roll in a vehicle, but after 30,000 miles of use, most stock shocks are as good as dead, like the shocks on this Mustang. A shock doesn't have to leak fluid to have long since given up dampening force. |
For drag racing, specialty shocks play a big part in chassis dynamics. For our beloved door-slammers, front shocks with very soft rebound settings allow the front end to rise, changing the rate of weight transfer to the rear tires to improve traction. Adjustable shocks allow the chassis tuner to control the rate at which that weight transfers. | 
For a Pro Touring car, front and rear shocks control body roll during cornering. With custom spring rates, you need to then optimize the shocks to your particular combination. This is where single- (or even better, double) adjustable shocks allow you to fine-tune the chassis setup with the shocks. |