In general, paper can be composted.
It’s far better to recycle paper than compost it – but if you can’t recycle it for some reason, for example, your recycler won’t accept shredded paper, then you can compost it instead.
Paper can be a great addition to a compost heap that is prone to becoming too wet or too heavily “greens” (ie, filled with lots of fresh veg peelings or garden waste) — paper helps soak up excess moisture and if scrunched up or shredded, can stop the heap becoming too dense and help with airflow.
Glossy paper, such as photo paper, should not be composted though, in case it has been coated in plastic. Similarly, some people don’t like to compost anything that has been through a laser printer or is heavily coated in colour inks (such as printed leaflets) as the chemicals used in the printing process can be toxic to the compost heap.