According to Wikipedia: "Decorative concrete involves using concrete in roles that are not strictly related to its functional elements. Concrete is known for its great strength, especially when combined with steel rebar. Concrete can be used for, among other things, walls, floors and countertops that are structurally sound and also provide a decorative finish that resembles polished stone, with less cost for materials."

Decorative applications on existing concrete:

Concrete dyes:

Concrete "dyes" take many different forms and compositions and can be used on both residential and commercial concrete applications, including sound/retaining walls, bridges, countertops, floors etc.

 Acid Staining:

Acid staining is not dying or pigment-base coloring systems, but a chemical reaction. A mixture of water, salts and acid is applied to the concrete surface and later neutralized by a basic solution of ammonia and water. This chemical reaction with the existing minerals (primarily lime) in the concrete creates new colors on the concrete surface.

Water Based Staining:

Water Based Stains are similar to acid based stains in the sense that one can still achieve a translucent look like acid; some stains are able to achieve an opaque color and/or a translucent effect. The main difference is that acid stains react to the concrete and change the physical make up of the concrete material, whereas water based stains are more of a "coating" that bonds with the concrete.

1/4" Stamped Overlays:

Rubber imprinting tools stamps are impressed into thin pre-mixed concrete overlay material to create natural stone or brick textures. These rubber imprinting tools are manufactured from molds created from authentic stone or wood. Release agents are used to help release the stamps from the concrete without sticking. Release agents come in either a liquid or powder form.

Epoxy:

Applied over acid stained and/or overlays to seal and protect. Some epoxies are also colored.

Polishing:

Concrete can be polished with Mechanical grinders and diamond pads of increasing grit sizes. Diamond pads come in many grit or mesh sizes.

Engraving:

Existing concrete can be remodelled by cutting lines and grooves into its surface. Geometric patterns, straight or curved lines and custom designs can be cut directly into the surface of the concrete creating the look of tile, flagstone, cobblestone and many other common surface patterns.

Source: Wikipedia