The TSA has a whole list of items that you are and are not allowed to bring on a plane in your carry-on and checked baggage. Nail clippers and files are allowed in your carry-on, but anything larger like scissors or nail kits must be packed in your checked baggage. Polish is also allowed in limited quantities in your carry-on. You can bring up to 3.4 ounces, or 100 milliliters, per container as long as it's packed inside a quart-sized bag.