How do you use bcrypt for hashing passwords in PHP?

Every now and then I hear the advice "Use bcrypt for storing passwords in PHP, bcrypt rulllez!!!11"

HTTP authentication logout via PHP

What is the correct way to log out of HTTP authentication protected folder?

How to remove .htaccess password protection from a subdirectory

I have password protected my entire website using .htaccess but I would like to expose one of the sub directories so that it can be viewed without a password.