What kind of licensing/permission is required to play a song in a play?

When I was researching my blog post on copyright for choreographers, I stumbled on this excellent post that addresses a question many theatre directors have:

What kind of licensing/permission is required to play a song in a play?

Entertainment lawyer Gordon Firemark gives a very good summary of various scenarios, what types of rights are needed, and who should be contacted for those rights. I also encourage you to read through the comments at the end of the post. There are some very good questions and answers in there too.