Very slowly! Dr. Brian Anderson, who teaches chemistry at the University of Texas at Austin, explained that many things we throw away decompose when they are eaten by tiny living organisms, such as bacteria or fungi. These living things can eat a piece of wood, leather, or cotton because the smallest parts (atoms) in those materials are still linked to one another in the same ways that they are in nature. Bacteria can break those links as they eat the object.
Plastics contain many of the same kinds of atoms as other objects. But in plastics, these atoms are linked to one another in more complicated ways. Bacteria can't decompose plastics because they can't break the links. Slower processes can break plastics down. But these processes can take decades or even centuries to do the job.
In the future, will we be able to use natural processes to decompose plastics? No one knows, but there is a ray of hope. Some fungi can eat a few types of plastics. Scientists are working to learn their secrets and to apply them to the millions of tons of plastic that wind up in our landfills.