How to eliminate aphids?

Aphids are, in my experience, common when there's something like relative nitrogen excess vs phosphorus, or imbalance, along with low lighting, temperatures and low humidity. From what I've seen though, while the conditions tend to be like that, the aphids just return practically instantly if they're removed. Removing them? I don't really know, some plant oils, acids, nearby aromas (mostly as deterrents, like the basil hempkid mentioned) could work.

There is all sorts of chemicals to kill them. Organic you can buy lady bugs. I grow basil around my plants and I never have any critters in my plants.

Do you have many? Take off as many as you can by hand. Check if you have eggs under the leaves, it's important. It depends on many opinions, but there's a solution, don't worry.