Oxygen sensor: All modern fuel injected cars utilize an oxygen sensor to measure how much oxygen is present in the exhaust. From this the computer can add or subtract fuel to obtain the correct mixture for maximum fuel economy. The oxygen sensor is mounted in the exhaust manifold or close to it in the exhaust pipe.
Catalytic converter: This muffler like part converts harmful carbon monoxide and hydrocarbons to water vapor and carbon dioxide. Some converters also reduce harmful nitrogen oxides. The converter is mounted between the exhaust manifold and the muffler.
Muffler: The muffler serves to quiet the exhaust down to acceptable levels. Remember that the combustion process is a series of explosions that create a lot of noise. Most mufflers use baffles to bounce the exhaust around dissipating the energy and quieting the noise. Some mufflers also use fiberglass packing, which absorbs the sound energy as the gases flow through.
Exhaust Pipe: Between all of the above mentioned parts is the exhaust pipe which carries the gas through its journey out your tail pipe. Exhaust tubing is usually made of steel but can be stainless steel (which lasts longer due to its corrosion resistance) or aluminized steel tubing. Aluminized steel has better corrosion resistance than plain steel but not better than stainless steel. It is however cheaper than stainless steel.
Common Problems: Well the worst enemy of your exhaust system is corrosion.... or more commonly known as rust. Rust is caused by moisture reacting with the iron in the steel and forming iron oxide. Moisture or water vapor is present in the exhaust as a by-product of combustion and the catalytic converter. Moisture can also come from the outside in the form of rain or snow.
Short trips in your car can shorten the life of your exhaust system. When you shut down your engine whatever water vapor is in the pipes condenses and turns back into a liquid. On a short trip the water never has a chance to get hot enough to turn back into water vapor and just stays in the system and rusts away the pipes. If you drive for short distances consider replacing your exhaust system with stainless steel when the plain steel one rusts through. If you drive more than 15 miles at a time then you should not have to worry about this.
If you live in an area, which uses salt on the roads in the wintertime, make sure to wash the underside of your car with water every few weeks. Salt speeds up the corrosion process and getting it off as soon as possible will help stop the corrosion. Make sure you run the engine after washing to drive off all of the water on the pipes.
On rare occasions the catalytic converter will become clogged and need to be replaced. Symptoms include loss of power, heat coming from the floor of your car, glowing red converter or a sulfur smell. Never let a mechanic tell you that you can do without the catalytic converter. Removing this component is illegal in most states and can lead to a hefty fine to the government if you are not careful.