With the advances made in the aquarium hobby in the last few decades, filtration types have reached what would have been considered impossible levels of effectiveness. Today one can purchase filtration systems which can perform mechanical, chemical, and biological filtration in one unit, as well as the accompanying oxygenation. One can even purchase a nitrate filter which can effectively eliminate the end product of biological filtration. These filters require additional maintenance and are easily neglected. There is an alternative nitrate filter which is not unsightly, requires minimal maintenance and tolerates a fair degree of neglect - live plants.
Live plants are an excellent filtration system, as well as being attractive in a tank.
Most fast growing plants are relatively heavy feeders and so are quite effective at removing nitrate from the aquarium water. Some good examples of nitrate removing plants are Hygrophila species and Amazon Swordplants for freshwater, and Caulerpa species for marine aquaria. Keeping plants in the tank with your fish is not always feasible. An example would be if the tank's occupants were largely herbivorous, like pacus or tangs. This could be as simple as having a well lit tank close enough to the tank to be filtered for a circulation of water between the two tanks.