Recursion

When to use recursion? What is the cue when you have to use recursion?

Suppose I am to write a program that computes a factorial or checks if a string is a palindrome or prints all numbers from a certain range? I could use loops for those but I could use recursion?

What's the advantage of either? Is there something that recursion could do that loops could not?

Recursion is required to deal with nested structures, such as trees. Furthermore, functional programming language fetishists have a strong dislike for loops because they require state management (temporary loop variable) and thus will always consider recursion cleaner.