All of the organisms in your composter and wormery need air and a great way to introduce this is to add scrunched up paper and cardboard.
Rather than cutting the paper or cardboard, tear into strips and scrunch into balls so that there are lots of air pockets. Torn up egg boxes are perfect.
When air isn't present in a composter or wormery, the contents become compacted and slimy and the conditions become what is known as anaerobic. Living organisms are unable to survive in these conditions.