Waxes, oils, naphtha, turpentine, ethylene glycol, and vegetable gums.
Shoe polish was originally invented as a waterproofing material for leather shoes. Later, the practice of buffing and polishing the leather made shoe polish that shined into an important fashion item.
Waxes like carnauba wax and beeswax help repel water and add shine. But to help them attach to leather, emulsifiers like lanolin and ethylene glycol are added. These also allow the waxes, oils, and solvents to mix with water to form a thick butter-like emulsion that makes the waxy paste easier to apply to shoes.
To thicken the emulsion, vegetable gums such as gum arabic are added.
Naphtha is a petroleum based solvent the dissolves the wax to make it easier to apply. Turpentine is a similar solvent distilled from the sap of pine trees. Both of these dry quickly, allowing the waxes to harden on the surface of the leather while retaining their shiny hard surfaces.
Shoe polish is colored by adding a form of fine carbon particles called lampblack (for black polish) and other dyes or pigments for other colors.