How does a pigeon avoid being lunch for a peregrine falcon?
He flies fast, he stays in a flock for protection, and he (quite literally!) keeps an eye out for danger.
Pigeons have such a wide field of view that they can see danger coming from almost any direction. There's only a narrow place in front of them where both eyes focus and a narrow blind spot in the back. Pigeons are not alone. Many prey species have a wide field of view.
This is hard for us to imagine because our eyesight is like the raptor's but raptors seem to know how it works. When a peregrine wants to sneak up on a pigeon he flies in the pigeon's blind spot.
Read more about what the pigeon sees in this vintage article: Anatomy: Field of View
(illustration from Wikimedia Commons; click on the image to see the original)