I expect that you have multiple problems, since not many pests eat both the root and leaves of carrots. It's hard to tell from the photo, but it appears that he largest carrot has been attacked by carrot fly larvae. They often make a ring of small darkened tunnels around the root. However, they don't eat the leaves or remove large portions of the root. Lots of herbivores like to munch the leaves.
Thanks vitog. My question was mostly about the leaves and large chunks of the root being eaten. I know I have squirrels in the garden. They like my strawberries and plums, and of course I don't have to bother with picking my hazelnuts myself. I have also seen something looking like chipmunks jumping through the garden. They are very small though, so it is hard to imagine they can do this kind of damage. On the other hand, I am quite sure I don't have rabbits or any other, bigger animals in the garden. Is it possible that squirrels or chipmunks are the culprits? As for the dark ring, I thought it was done by the carrot rust fly larvae, is it what you have in mind as well?
I started paying more attention and indeed saw something looking like a mouse or a vole (probably a vole, more bulky and with much shorter tail than a mouse), scurrying through my edible garden. Must be more of them since I was able to see one. I don't like having them in the garden, but so far I can live with the damage they are doing. Well, will see what will happen next year. Definitely, life of a gardener is not an easy one! What is eating the leaves is still a question mark.
