Rats are well known for many detriments to humans. At the forefront of these detriments is the fact that rats carry the plague virus. They also carry tetanus, leprosy, trichinosis, and salmonella. This prevalence for disease leads to rats, Norway and Roof, contaminating food sources just by feeding off of them, e.g. your grain and feed stocks.
As far as structural damage rats can do great harm. This includes damage done by gnawing and burrowing in and around foundations for homes and other structures. They will gnaw on electrical wires, wood framing along doorways, windows, and even do damage to metal structures! Rats cause problems to humans by tearing up insulation inside walls for use as nesting materials, too. Woodrats will tear up furniture and mattresses of campers and cars!