If you own a newer vehicle with factory alloy wheels (and they are not chromed or chrome-clad) – chances are they are clear coated. Automotive wheels are subject to severe conditions; heat, road-level debris, salt, grit and chemicals. Car manufacturers understand this, and coat the wheels with a plasticized, softer and thicker, and responds to other luster-improving chemicals better than regular paint polish.
Start by cleaning those wheels using the same car soap you used for the rest of the car (a stronger mix is fine for brake-baked and grimy wheels). To improve the shine and luster of clear coated wheels, use a plastic polish like Mothers Plastic Polish or PowerPlastic 4Lights on them. The plasticized paint on your wheels will respond best to a plastic polish, though any cleaner wax will help clean, clarify and protect.
When dealing with any automotive wheel, refer to the wheel section in this guide: it offers a collection of solutions for almost every type of wheel, including non-coated aluminum (use Mothers’ world-famous Mag & Aluminum Polish), chrome plated (try Mothers Chrome Polish), and a host of other wheel types. Take time to study the Detail Guide for help deciphering exactly what sort of wheels you have, and the many caveats for cleaning them all – their finishes can be complicated, can be easily marred, and are expensive to fix.