Do you really know what you should and should not compost? Here is a list of 13 things you should compost… Fruit scraps but not citrus. Vegetable scraps. Coffee grounds. Tea leaves or tea bags. Eggshells. Straw. Shredded Paper. Newspaper but not the glossy pages. Cardboard. Grass cuttings. Plant cuttings. Dried or fresh leaves. Sawdust.