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?

Been a while since I've had to look into it, but don't the fastest sorting algorithms still use recursion?