Root maggots, Most often called Cabbage root magots but they attach most brassicas and are most detrimental to root types like turnips and radishes. To be honest control is quite difficult. Here is article from the U of Illinois. No insecticides currently available to home gardeners.

Here is a link that might be useful: Root maggot

I hate those little critters.
Unfortunately there is no good way to get rid of root maggots once they're there. You have to keep the fly from laying in the first place and this can be easily done by covering the growing radish with light-weight row cover.

But fear not, most of the radish will still be fine if you cut away the bad parts.

-Mark

I read somewhere that planting garlic before the radishes or other crop deters them, has anyone had success with this?

Thanks for helping!