Covers are really for people. Covers will help keep odors within the box although you may need to hold your breath when you remove the top. Some covers have vents at the top into which you can put charcoal filters to absorb odors. Most covered boxes are made of plastic although we have seen decorated cardboard covers sold separately. Manual, semiautomatic or automatic Manual boxes require you to scoop out the soiled litter.
Semiautomatic boxes have some sort of mechanism to help remove the clumps.
Some boxes have a removable pan with holes in the bottom. Lift the pan and the clumps stay on top, the rest of the litter spills out through the holes and into a fresh pan below. Some boxes need to be flipped on their sides so that the clumps fall into a container attached to the side. Turn the box right side up, slide the container out and throw away the clumps. The containers are then emptied or thrown away.