Fish swimming around in the wide open spaces don't have a problem that fishes have while swimming in confined tanks. That particular problem is scientifically known as "ka-kah" (another fish term meaning "fish waste").
Ka-kah, and other waste products, decays and releases ammonia into the environment. And even the smallest amounts of ammonia can be deadly. (Don't let the fish "get" ammonia!)

The types and makes of filters are vast, and the decision about which one to use depends on the aquarium environment and the type of fish. After reading all I could sanely digest, I went to my local fish store. My limited knowledge, and their more vast knowledge and experience, convinced me to purchase canister filter with a wet/dry biological filter device. My particular unit came with a gravel washer (or vacuum).
This seemed to be the most effective filter system available. I did consider strictly using a purely natural biological filters, or chemical filtration. Pure biological filters by themselves, while natural, can only support small fish populations. And, I really don't care to use any more chemicals than necessary (I already have to deal chemically with the chlorine problem).
As with any filtration system, I still need to clean the gravel on a regular basis. This is where I use the vacuum. Bits of decaying matter get caught in the gravel, and need to be removed to prevent an ammonia build-up.
One last thing before the fish arrive. Click Spruce It Up. The following will get you back the start: Let's Get Some Fish!