Exhaust Systems

The Exhaust system is an often misunderstood part of the engine. It does a lot more than just remove the waste gasses!
There are a number of design requirements when creating an exhaust system for a vehicle. Modern systems are centered around increasing performance, lowering emissions, and reducing noise. Noise is controlled by designing baffles and resonators which are able to cancel out certain noise frequencies. The noise from each cylinder firing event can be controlled and timed to reflect back against each other, pass through padding which can absorb some noise and also resonate to provide an acceptable sound.

Emissions are controlled by Catalytic Converters which are able to induce a chemical reaction in the hot gasses to reduce pollutants, such as combining Carbon Monoxide (CO) with "spare" Oxygen to produce CO2. Nitrous Oxides (referred to as a group NOx) and Hydrocarbons can also be reduced. The Catalytic converters need to be hot to function correctly which has introduced a few methods of quick heating. Some early systems had electric heaters inside which would get the Cats to operating temperature quicker. Modern designs will place the Converters as close as possible to the cylinder head, and you may also see twin wall exhaust pipes designed to insulate the exhaust gasses so the heat is passed to the converter matrix. Emission control Air Pumps are also used under cold start conditions. The extra fuel which is needed to ensure combustion at low engine temperatures has extra air added to it in the exhaust system to promote it burning on the catalytic converter matrix, both heating the Cat quicker, and burning off the unused Hydrocarbons.
Diesel Technology also uses Catalytic converters, and often Diesel Particulate Filters known as DPF, FAP and other manufacturer specific names. Particulate Filters capture soot and ash from the exhaust gas stream and store it in a fine sponge-like matrix. When conditions are right, the Diesel engine ECU will activate methods to increase the Exhaust Gas Temperatures to burn off the collected soot. If these occasional Regeneration phases can't be activated, the filter may clog beyond repair and require replacing.

Tuning the Exhaust System

Increased power from the engine due to exhaust tuning is often the main goal of the Tuner. To start with, you need to know how the final Performance aspect of the exhaust system works. The First and most important thing is that there is never a need for "Backpressure" for performance. There is a theory, based on the noted effects which seems to point to backpressure being important, but that isn't the case.
To produce power, you need to maximise the efficiency of the engine, which can include a greater turnover of air and fuel passing through. If you can get the exhaust gasses out easier, you can get more air and fuel into the engine to produce more power. Any backpressure will reduce the amount of air and fuel that can fill the cylinder and reduce the power. That would also point to the most powerful exhaust systems being entirely open from the exhaust valves, but that is not the best design.

The Missing Link is Exhaust Tuning. This is probably the closest or purest type of "tuning" to the name, as you are dealing with the same tones and frequencies as in music.
So, What is happening? The exhaust gasses pass out in pulses from each firing cylinder. Each pulse is a high pressure area, with a low pressure area behind. You can visualise this by looking at ocean waves, the peak representing the high pressure area, and a trough behind that is lower than the average ocean height is the low pressure area. The exhaust pipes can be thought of like an Organ pipe. For each diameter and length, there is a resonant frequency, in the same way Organ pipes are different sizes and diameters to produce different notes.
Exhaust tuning uses this resonance to help evacuate the gasses from the cylinders.
This is the main point.
A finely tuned exhaust not only reduces the back pressure to minimal levels, it can actually pull the gasses out of the cylinders!
When correctly designed, the exhaust can be tuned to resonate and the pressure vibrations in the exhaust can be timed to have a low pressure wave arrive at an exhaust valve as it opens, pulling the gasses out. This tuning isn't something you can easily modify without advanced modeling of fluid dynamics but many performance systems are set up with this in mind.
The exhaust manifold is the major component responsible for exhaust tuning. The length and diameters of each pipe can be prepared to create a resonant effect over a certain RPM range. It is worth noting that unless the diameter or length changes, the resonant RPM band is fixed. When the engine is at the specific RPM range to match the exhaust frequency, the tuning comes into play. This effect will boost the torque at that RPM range although it may also reduce power at other RPMs. When exhaust systems are quickly modified by adding different rear silencers, or larger diameter pipes, the tuning can be disrupted. In a similar fashion, you wouldn't cut the last metre from a Church organ and replace it with a larger pipe without expecting the sound to change!
It is often these changes that disrupt the resonance and tuning in an exhaust system that are noted for a reduce power output. Without understanding the resonance effect, often the incorrect conclusion that the free-flowing exhaust has created the problem by being too free-flowing.

Performance Exhaust systems are therefore something that can not be easily designed. There are always compromises somewhere, with the first to go usually being the silencing effect. If you are looking at buying a new performance system, you should look out for changes to the design that would be beneficial. For example, updated equal-length exhaust manifold primary pipes, or repositioned X sections on "V" engine exhausts. Larger diameter pipes may change the sound, but it is often unlikely you will notice any improvements to the power. Likewise, Stainless steel exhaust manifolds that follow the design of the original will not provide any improvements as they will not fundamentally change the exhaust tuning.