Red ants, or fire ants, first showed up in the United States after the second World War and are thought to have been brought in with woody plants that are often used for landscaping. (References 1) Since they not native to the U.S. they have no natural predators, and they've been able to spread practically unchecked into all areas of the States.
While many chemicals have been developed over the years to control red ants, these can be dangerous to pets and children. Many organic ways to get rid of red ants exist, and most work by interrupting or overriding the scent tracking ants use to follow their trails.
Black or Red Pepper
Track a line of red ants to find where they are entering your home, then spread a line of black pepper or red cayenne pepper across that entry spot. The ants will refuse to cross the line of pepper.
This can be done outside as well, but the pepper may be blown away in the wind.
Mix one part water with one part white or apple cider vinegar and add the mixture to a spray bottle. Wipe down all surfaces and counters with the mixture after you clean each day to ensure all food scents are eliminated.
Locate where the ants are entering your home and spray the area liberally with the vinegar and water mixture as well. Vinegar is a natural deodorizer that will remove the ant scent and make them lose their trail.
Cream of Wheat
Sprinkle dry Cream of Wheat cereal into and around an ant hill outside. The ants will collect the grains as food and take them inside their nest. As the grains are eaten, they mix with the moisture inside the ants and swell up, causing the ant to "explode."
Plant mint or peppermint all around the outside of your home to prevent ants from entering. Alternatively sprinkle crushed dried mint leaves at the location where the ants are entering your home.
Another way to use mint is to mix mint or peppermint into a spray bottle with water, then spray the entry point liberally to prevent the ants from entering in the future.
Heat a large pot of water to a rolling boil, then carefully pour the boiling water directly into the ant hill outside. Some say this is only a temporary fix and that the ants may simply create a new ant hill in another location of the yard.