I call it 'marking'. I say,"I have some marking to do."

From England I would say 'marking exams'.

Grading papers is American terminology and in England we mark exams/tests

I'm not an actual teacher so I'm probably not qualified to answer this. From my college days, my professors usually referred to it as "grading papers". Checking/grading tests is another I would hear often. There are other phrases used but those three are the most common ones I recall hearing.