fasting?

So I stumbled upon this article online: Your Church Is Dying Because You’re Afraid to Do These 6 Things. I was struck by “1. Enter a Time of Corporate Prayer and Fasting”. (And, tbh, the rest is pretty average.) So I was wondering, fasting?

I have also found an interesting article online: The Fall and Rise of Fasting in the British Reformations. It gives a historical English account from the time of the Reformation.

Third I was always wondered by the Book of Common Prayer (1662) includes Tables and Rules for the Feasts and Fasts through the whole Year. And what authority does this have for modern users of the BCP?

So, my question: what role should fasting play in the life of a modern follower of Jesus??