The skin around our eyes needs exfoliation just like everywhere else. Yes, it may be thinner, more delicate skin – but a gentle granular exfoliant (never an enzyme-based exfoliant as this is way too harsh around the thin skin of the eyes), ideally in a nourishing base like oil will help keep your eyes bright and hydrated.
Ensure you don’t over-exfoliate, once a week is plenty. And always ensure you massage exfoliant in very gently, especially around the delicate eye area. While you’re at it, do the same for your lips, and finish with a nice, thick occluding moisturiser (an occluding moisturiser creates a barrier on the skin, which holds moisture beneath).
And don’t forget to apply sunscreen to the area every day, especially when exfoliating – it makes skin more vulnerable to sun damage.