If your cat tree comes with removable covers that are washing machine safe, definitely toss them in the machine from time to time to keep everything clean and tidy. If the materials are removable but cannot be machine washed, soak them in a mixture of warm water and mild detergent and give them a little scrub. If none of the materials are removable, you can always vacuum the tree first and then use a damp microfiber cloth with a pet safe cleaning agent to remove any dirt and hair. There are also special pet hair removal brushes that are highly effective at removing fur hairs from carpets and other textiles.\r