Each cleaner has it's own purpose but common cleaners are snails, hermit crabs, and variety of shrimps.
Snails tend to clean the hair algae and algae off the glas
Hermit crabs tend to eat left over food from the fish
Cleaner shrimp keep parasites off your fish
Peppermint shrimp are by far my favorite keeping apatasia out of your tank. Apatasia are an anemone like specie that stings your corals causing them to die. Peppermint shrimp keep your tank clean of it. There are brands that sell apatasia meds that kill it but IMO it can't get all of it like peppermint shrimp and there is no more natural way then putting one of these buggers in your tank.
Then there is the emreled crab IMO underrated cleaner. Mine cleans very well but can't get to some spots the snails can but vice versa gets into the places the snails can't get to. But if you do add one of these be warned they will climb on the corals making toppling them over, they love to climb they are very curious. They will clean the new piece of coral you put in and the rock around it make sure you use some aquraim safe putty or glue and glue it to the rock stopping him from toppling the coral over.