Methods and apparatus for treating water and wastewater include the step of flowing a suspended solids stream generally upward through a sludge blanket region of a cloth disk filter vessel, thus forming a partially treated effluent composition and a solids-enriched sludge blanket. The partially treated effluent composition is allowed to flow generally upward to a cloth filter zone in the vessel after contacting the sludge blanket. The methods include flowing the suspended solids stream through one or more distribution headers positioned in the sludge blanket. An option is to provide a sludge concentration zone in the sludge blanket region, allowing sludge to flow into the sludge concentration zone to form concentrated sludge. Other methods and apparatus include backwash assemblies that backwash substantially the entire filter cassette surfaces, with or without use of a sludge blanket zone. Either the backwash assemblies or filter cassettes move in the latter methods and apparatus.