There are several filtration techniques that have been shown to work. It is very difficult to say which method is the best since they are different approaches to the same problem.

Berlin Method
This method was made popular by the Berlin Aquarium Society, and was aptly named. Berlin systems consisted of a tank mainly filtered by live rock and a protein skimmer. The live rock acts as a natural biological filter. The porous rock makes a good home for aerobic nitrogen processing bacteria. The low oxygen centers of the larger rocks provide a place for hypoxic bacteria to denitrify the water and complete the nitrogen cycle. The protein skimmer acts as a mechanical filter of sorts. It removes dissolved organic compounds from the water before they can break down into nitrogenous waste. This system relies to a large extent on strong water flow to move water in and around the rocks.

Jaubert Method / Deep Sand Bed Method
Dr. Jean Jaubert at the Musee Oceanographique in Monaco developed what is known today as the Jaubert Method. He discovered a means of de-nitrification through the use of a plenum and used it with great success in his public aquariums. The plenum acted as a physical barrier where water could diffuse into a low oxygen area where hypoxic bacteria could flourish. The bacteria would break down nitrates into nitrogen gas to complete the nitrogen cycle. It is debated whether the plenum is necessary at all, and in some cases is actually a detriment. Many aquarists today have found that an adequately deep sand bed provides low oxygen areas for de-nitrification.

Algae Filters
Algae filters are not small gadgets used to clean the aquarium's glass. They are separate filters where algae is grown and harvested as a method of filtration. Algae binds nitrogenous waste as well as heavy metals and phosphate. By periodically harvesting the algae, the aquarist is removing concentrated waste from the reef system. As a side benefit to filtration, algae filters become refugiums and are a home to beneficial micro-fauna such as amphipods and copepods. Sometimes those invertebrates are reintroduced back into the display tank and make a healthy snack for a fish or coral. A super powered version of the algae filter was developed by Dr. Walter Adey of the Smithsonian. Instead of using macro algae, he cultivated algal turfs that are many times more efficient at binding excess nutrients. Turf algae, however, require thrashing surges, so the Adey style algal filters always incorporated a strong surge device along with high intensity lighting. Home models are available; however, are very expensive.

The filtration methods above are not mutually exclusive. It is possible to incorporate all of these filtration methodologies in the same tank. It is not uncommon to see a reef setup with live rock, skimmer, deep sand bed, and a gravity fed refugium. Which filtration method is right for you depends in large part to the type of habitat you are trying to reproduce and what types of inhabitants you intend to keep.