In most reefs and many FOWLR, organisms like copopods, bristleworms, starfish, snails, crabs, and shrimp are the mechanical filters. They consume wastes and uneaten food, further breaking it down and removing some of the nutrients from the system (well, not removing but binding them in the form of more worm, star, snails, crab or shrimp). Since these animals come in a variety of sizes and food preferences, a diverse mix will result in very little waste that decays in the system. Mechanical filters can be used as well, as long as they do not trap detritus where the critters can't get to it--one reason why wet-dry setups can cause nitrate spikes in systems is that the bio-ball media doesn't provide great access to the detrivores. Sponges prefiltering water in advance of a wet-dry resolve this concern, but still require monitoring.
The live rock and sand are the media for the biological filtration, often supplemented with algaes--macros like chaeto, and coralline algae as well. I usually leave the entire back and one side of my tank uncleaned--allowing the hair algaes to grow, which helps reduce nitrates, as well as providing good grazing ground for the herbivores, and improving pod reproduction.