An aquarium filtering and purifying system includes an upper display tank and a lower filter tank. The water from the upper tank can be delivered to the lower tank to a filter, such as within a surrounding filter fabric or membrane, such as a filter sock. An air tube can also be inserted into the filter tank to an unfiltered side of the filter, such as within the filter sock, to deliver air bubbles into the filter tank. The air tube can have an air stone at the end thereof to diffuse the air bubbles. Further air stones can be provided on an outside of the sock in the first compartment. Filtered water is delivered to a second compartment in the filter tank. The next compartment can have sand, and/or rocks and/or algae and/or a clean-up crew to assist in purifying the water. Water from the second compartment then passes to a third compartment, through a bubble trap, and then is pumped back to the display tank. Alternatively, the first compartment can be provided with a macro algae bed instead of a filter sock.