A strop is a length of material, usually leather or cotton, used to realign the edge before shaving.
The most common type of strop is the hanging strop. Usually made of leather or cotton it is a long rectangle of material. One end of the strop is hung from a hook or something else, while the other end is held and pulled taut with a hand.
Comes in a variety of sizes. Its main advantage is its use while traveling. Easily stored in luggage for long or short trips. Typically shorter than the hanging strop. There is no need to create tension as it is inheritanly built-in which creates somewhat of an advantage for the beginner by removing this variable. Paddle strops can be two-sided or four-sided. Can have various leathers attached or wool felts for applying abrasives. Commonly used after honing to refine the edge with diamond or chromium oxide pastes.
The most common, and most used, material for strops is leather. Leather provides a soft and smooth surface which gently aligns the edge of a straight razor. It is only used in both hanging and paddle strops.
The textile type of strop is often called linen, but few modern strops use actual linen. The most common material used is cotton. It is only used in hanging strops, not paddle strops.
Balsa wood is sometimes used on paddle strops instead of leather.
Recently Tony Miller of The Well Shaved Gentleman started producing a synthetic strop as an alternative to leather. The synthetic material is a nylon web core with a thermal polyurethane covering bonded to the core. Due to the material being non-pourous, it is not suited for use in a pasted paddle strop.