Aiptasia are bad because they will quickly spread throughout your tank and eventually sting and kill corals. IMO, when it takes over it's ugly too.
Here's a brief summary of your options:
1) Only one perfect option: You remove all of your rock with aiptasia on it and trade it in for new rock. Clean the tank and corals thoroughly before adding the new rock. Expensive but works.
2) Use true peppermint shrimp (Lysmata wurdemanni) to eat the smallest and medium sized aips. They probably won't eat the large ones. The trick is not to add any food to the tank so they have to eat the aips. So if you have fish, most of the time the shrimp will eat the fish food and not the aips. You can get these as guaranteed Lysmata wurdemanni from some online vendors if you tell him you want this shrimp specifically. Most stores don't know what they have. Even the right peppermint shrimp are not always dependable.
3) You can try a copperband or racoon butterfly or other butterfly. They can be hard to acclimate and keep. They don't necessarily eat the aips and may eat your soft corals. It can take up to two months before you know if they will eat aips, and they usually don't eat the big ones. They may also eat majano anemones.
4) Berghia nudibranchs eat only aiptasia. If you get enough they should take care of the problem. They are not 100% successful in every tank. When they don't work I think they are either eaten by something or the person did not buy enough so the aips multiply faster than the berghia can eat them.
5) Most of the chemicals, like Joes Juice, frequently make the aip problem worse not better. If you use chemicals you should siphon off the dying aip parts to make sure they are not going to create more.
That's the summary of options in brief. Aiptasia have an amazing capacity to survive. They like perfect water conditions (light, food, water quality) but don't require it to thrive. I wish all things saltwater are this easy to keep.
If you want to know more, I am happy to help. Just PM me. Good luck.