I've quite some experience at dealing with rats and mice.

Basically, rats can be regarded as bigger, but far, far more intelligent, mice. Both urinate and defecate all over the place, including the places that they, and we, eat. Both, but particularly rats, carry diseases, rats ones that can kill a human, such as Bubonic Plague (Black Death), which is a caused by a bacterium living in the fleas carried by rats, which also bite humans, and Weil's Disease, passed on by rats urinating in drinking water, or water that might be accidentally ingested, such as river water where people swim.

With both, prevention is better than cure. You need to ensure that there is minimal ground cover close to buildings - leave a foot clear of plants around barns and garages, and mow any grass close to buildings sufficiently short that it can't act as cover. Find out where the vermin is getting into buildings, and block the holes appropriately, for example with cement.

For both, trapping usually works, but rats may be very suspicious of an unusual and too easy source of food suddenly appearing in their environment, particularly if it smells of human. I sometimes think it is better not to set a trap for a couple of nights until they get used to taking the food off it, then set it.

For a humourous take also containing useful tips you might want to read my posts as Java Jive in these threads ...

About 16 or 17 posts down, beginning: "Mice are (at least) two problems in one ..."
uk.d-i-y - Help get rid of mice

My second post beginning: "Ah! Now that takes me back ..."
uk.tech.digital-tv - Digital Upgrade