Oracle index analyze stats – managed by whom?

a question about managing indexes.

In what cases do indexes stop being analyzed?

What’s the way to get indexes analyzed automatically?

Do I still need to manage index analysis somehow manually if they break? How can they break? How do I know they are broken? How to fix? In what intervals?

Perhaps there’s no auto-management? This would be very surprising. But if this is the case, how to manage indexes manually? Thanks.