A Guide To Transclusion in AngularJS

I've always had a problem with transclusion. Though I've used it from time to time, using it always felt uncomfortable. I was never really sure what exactly the API was doing, or more importantly, what exactly I was supposed to do when using it.

Based on what I've heard, I'm not alone in this. Transclusion is one of those things people often mention when they talk about their difficulties with Angular.

What is it that makes this a difficult topic then? Conceptually we're not talking about any...