[Source]
There are many different filtration devices available for purchase today. They are made to clean and aerate the aquarium's water. Below is a brief description of a few.
Undergravel filters are virtually maintenance-free for long periods of time. They depend on water being drawn from underneath a filter plate, either w/ an airlift tube consisting of a vertical tube into which air bubbles are released via an airstone, or with the use of a powerhead. The aquarium's water is drawn down into the gravel bed, which not only filters the water mechanically but allows bacteria buildup in the gravel that is essential to the aquarium's well-being. The bacteria will break down and nitrify the waste material.
The effectiveness of an undergravel system depends on the nature of the gravel substrate you are using. The more porous the substrate the more effective the entire process will be.
Powerheads are used to provide a constant steady flow of water through the undergravel bed with aeration and surface agitation. You can purchase a reverse-flow powerhead to push the water back down the vertical tube and send the water upwards through the gravel. ( I have tried both ways and they have worked great!)
Outside Filters provide mechanical filtation by removing and filtering waste from the water. They usually do this by replaceable filter media such as carbon or floss or cartridges that you buy already containing the necessary items. Many of them have extra media containers for adding extra carbon or etc.
Inside Filters are air-operated filters that remove dirt mechanically. They provide water circulation as well as water aeration. They usually consist of filter wool and carbon. The wool traps the small dirt particles yet allows water movement through the filter. The carbon is used to absorb waste material and help purify the water.
Basically no noise, realtively cheap and almost no maintenance. PennPlax makes a decent box filter. They require carbon and cotton. These filters sit on the bottom of the tank.