undergravel (UG)

concept
Increase the amount of surface area for beneficial bacteria to live on by using the substrate in the aquarium.

Use the substrate to trap detritus(crap) to improve water clarity.

in practice
Undergravel filters are defined by using the substrate to filter the water. This type of filter can take on many forms.

The typical UG consists of a filter "plate" (some kind of plastic with slits for water flow) that sits on the bottom of the tank. Some form of tubes are put into the filter plate and an aerator(s) is placed at the base of the tubes. The aerators drive air into the tube and pushes water up out of the tube which creates water flow down into the substrate into the filter plate and then up through the tube.

in practice - variations
Variations of this filter come from changing the way you drive the water flow. You can attach a power head or water pump to the top of the tubing or even jam a canister filter's intake into the tube to drive water flow.

in practice - considerations

size - substrate
If the substrate is too fine, the water flow may get clogged easily.
If the substrate is too large, particles will easily pass through the filtration system and dump detritus on top of your life until the filter becomes more "mature" and starts to clog up.

amount - substrate
If there isn't enough substrate, you may not provide enough surface area for bacteria. If there is too much, it may become difficult to clean and water flow may be impeded.

gravel vacuuming
This filtration system requires gravel vacuuming to have the tank survive in the long run. Leaving detritus to build up in your gravel bed will likely end in dead fish from steadily increasing leaching of nitrates into the water column.

shut off
Detritus WILL build up underneath the filter plate, and turning off any mature UG system means you should probably take everything out, clean it, and re-cycle the tank. UGs that are packed down enough with detritus can have very poor water circulation if they're turned off which may cause anaerobic bacteria to thrive and create concentrations of dangerous chemicals.

pros 'n cons

sand
Sand is a no-no unless you rig a filter plate fine enough that you're not spitting sand all over the place or clogging your water flow from the fine grains.

And you don't want sand near filtration/flow units if you can help it, it may damage propellers in the long run.

powered UG
If you're using a power head/canister/pump be aware that higher flow rates are going to build "gravity" in your tank. When I first installed it in my 40 gallon, my turtles and fish looked like they were having trouble adjusting. (It might be good exercise though, hah)

planted tanks
There are reports of plants not doing as well in UG filtration comparative to other filtration methods, but I haven't tried it myself. In theory, the UG should hold more detritus and the plants should eventually be using those nitrates as a nutrient source. But, I have also read mention that the water flow at the root structure is too fast to absorb nutrients from the water column.

Although, it is obvious that plants with large root structures will start to push into the filter plate and start to impede flow.

it's shit
You have to be okay with intentionally building crap up on the bottom of the tank. There are lots of people that just can't stand the idea.

breeding
This filtration system is great for breeding. Small fry or whatever can't get sucked away as easily as a normal filter.