We use a lot of different materials for bandaging:
1) Rolled cotton; 2) 2" cast padding; 3) 4" cast padding. Dogs' (and cats') limbs have very little tissue on them aside from bone and blood vessels, so in order to apply bandages that don't restrict blood flow, we have to use large amounts of padded material.
4) 4" adhesive elastic bandage; 5) 2" adhesive elastic bandage. These are used both to wrap the top and bottom of bandages (on larger bandages) or to wrap the full length of the bandages (on smaller bandages). We are very careful when using this material, because- since it is elastic- if it is applied improperly, it can also restrict blood flow in the limbs. We stretch it out and lay it on the bandage site to avoid this possibility.
6) 3" brown gauze. This material is used as the second layer on the bandage- it's wrapped around the cotton padding to hold it in place. We also have 6" brown gauze for SUPER large bandages, but we go through this 3" stuff like crazy.
7) Telfa pads! These are little pads made out of a material like the white pad on a Band-Aid- it's designed not to stick to open wounds, so we use it to cover the wounds before applying the rest of the bandage. When the bandage is removed, ideally this pad won't stick to the wound like a piece of cotton might.
8) 2" elastic bandage; 9) 4" elastic bandage. Unlike the ADHESIVE elastic bandage on the left-hand side of the picture, this stuff sticks to itself but not as much to the underlying material, so we generally use it to cover the brown gauze on larger bandages, which are then anchored at top and bottom by adhesive elastic bandage. This material can also constrict and cause loss of blood flow, so we are very careful about applying it, too.
10) Bandage scissors, NeoPredef powder, and 1" medical tape. The odds and ends of the bandage toolkit- bandage scissors have a blunt end that allows them to be used safely to remove bandages without harming the underlying anatomy, NeoPredef powder contains a topical antibiotic, anti-inflammatory, and numbing agent, and medical tape is used in "stirrups" to keep (as much as possible) bandages on limbs from slipping down the limb.