I had tons of ant problems in our 1890's Edwardian when we first moved in. San Francisco is basically one big ant colony - Argentine ants arrived on a cargo ship at some point and turned the entire city into a giant anthill. After much trial and error, I figured out how to combat the problem by observing their behavior. I'd start out by scrubbing their scent trails with vinegar by beginning at the end of their trail and following it back to the source, vigorously scrubbing the whole way so new ants couldn't follow the now-dead ones back into the house. Once I found their entry holes, I filled them with Borax or diatomaceous earth and sealed them off with clear caulk, making Evil Mad Scientist voices while I did it. "MUA-HA-HA-HA!" It helped, along with going around inside and outside the house, finding their entryways and blocking them off with more Borax/diatomaceous earth and clear caulk.
Another way to impede the progression of ants is to get them to take poison back into their homes and feed it to the queen and the other ants in the colony. I made my own ant bait by dissolving ¼ cup honey with ¼ cup sugar in a heat-resistant glass jar in the microwave on high for one minute. After the sugars had dissolved, I added ¼ cup borax to this, stirring well. Then I went outside and placed a tablespoon of this mixture in the ant pathways and on the anthills. Ants are attracted to sugar, and since honey is sticky, it holds the borax and keeps it from blowing away in the wind. If it rains, be sure to reapply - borax loses its effectiveness if it gets wet. Ants think borax is food, but it's very toxic to them and they die after eating it.
You also have to be extremely vigilant about keeping your house and kitchen clean! Preventive measures include wiping down the counters, keeping the floors clean, not leaving food out, and keeping sugary foods well-sealed. Seal dry pet food in airtight containers.
Some people swear that sprinkling powdered cinnamon around the house and around the edges of the floors works, but I found it to be labor-intensive and expensive - you need a lot of cinnamon for this, and you have to reapply when it rains, when the wind blows, or when you vacuum. Also, the cinnamon blows around and makes a mess. I found the same issues with peppermint oil - it's costly and time-consuming, and I got tired of my house smelling like a candy cane. Clear caulk is really the way to go, you just apply it once and it's not going anywhere because it's waterproof, it doesn't fade or blow away, and the ants are simply just not going to get past it.
I haven't seen ants in years ... uh oh, I hope I am not jinxing myself now. *knocks wood*