As soon as they grab that succulent, unsuspecting insect, they need to blink, and it's not to keep their eyeballs from flying out. The eyelids pushes their eyes down to the top of their mouth and actually helps push the food down their throat. Talk about eyes bigger than their stomach.
Most frogs actually have teeth on their upper jaw, used primarily for keeping the prey in their mouth while it awaits the eyeball assault that pushes them down to the stomach.
If you were interested in what happened after the dinner starts its journey to the stomach, look no further than the glass frog which has translucent skin. That means you can see everything on the inside, including organs, bones, and muscles. Track that fly from the mouth, all the way to the stomach where it gets digested, like a grand tour of frog body.