Polyurethane is widely used in shoe construction, whether as inexpensive formal wear rentals or applied as a coating over patent leather. The gloss imparted by the plastic is designed to eliminate the need for constant polishing, but it may be required to buff out the occasional scuff or blemish. If so, a variety of materials may be used to perform this task.
Patent Leather Polish
Although traditional shoe polish is primarily designed for giving a sheen to regular leather, some specialized polishes incorporate compounds that are ideal for putting a gloss on polyurethane. Commercially available patent leather polish often contains silicone, itself an artificial ingredient that won't harm the poly finish. Applying the polish in a circular motion to the entire shoe, letting it absorb then buffing off the excess is effective for patent leather and polyurethane shoes.
Since polyurethane -- like all plastics -- is essentially oil-based, other oils found around the house or pantry work well to restore lost luster. Mineral oil and even petroleum jelly rubbed into the polyurethane footwear work well in giving the shoe its glow once more. Even acetone or nail polish remover on a cotton ball -- lightly applied to the shoe -- works well in removing tougher scuffs on purely polyurethane or faux patent leather footwear.
If the polyurethane or patent leather shoes are just dusty or dirty, specialized polishes and cleaners are really not needed. Simply wiping the shoe down with a damp cloth and a little laundry or dish detergent is effective in getting off most dirt and grime. Follow up with a microfiber cloth to remove any water spots, bringing out the shine expected from the shoe.
Polyurethane can scratch and scuff the same as any other plastic. Therefore, there are things you would use with regular leather shoes that you should not use with patent leather or poly shoes. For example, brushing the shoe with a horsehair brush prior to cleaning is de rigeur with leather but will scratch and swirl shiny polyurethane. However, like leather shoes, storing this footwear in shoe trees helps mitigate the inevitable creasing that occurs, letting the shoes keep their shape. Separate each shoe in the pair with a piece of tissue paper to prevent one from scratching the other in storage.