Cats can climb upwards, downwards and into or out of structures. They climb by utilising their claws which they can alternately extrude to grip onto the surface and then retract again to release their grip and move the limb higher or lower down the surface. Limb movements during climbing follow the same pattern as those used in walking, or occasionally may approximate a gallop (particularly seen when climbing tree trunks) (Beaver, 1992)

In the following video you can clearly see how the cat (after jumping onto the tree trunk and using his claws to grip the bark) pulls with the front limbs whilst pushing with the hind limbs to pull himself up the tree.