A differential category is a category enriched over commutative monoids together with a monad, equipped with some additional structure including a differential operator. I will review the notion of a differential category and then I will introduce variants I’ve been working on. These are respectively called graded, filtered, relative and Hasse-Schmidt differential categories. I will motivate each variant, explain the definition and give some examples and results. I will also mention some conjectures and difficulties which are not yet resolved.