“Thinking in AngularJS” if I have a jQuery background?

Suppose I’m familiar with developing client-side applications in jQuery, but now I’d like to start using AngularJS. Can you describe the paradigm shift that is necessary? Here are a few questions that might help you frame an answer:

How do I architect and design client-side web applications differently? What is the biggest difference?
What should I stop doing/using; What should I start doing/using instead?
Are there any server-side considerations/restrictions?

I’m not looking for a detailed comparison between jQuery and

It’s been a while, but from what I can recall, the jQuery applications I’ve worked on tended to end up as a pile of miscellaneous scripts without any imposed structure - a big mess. Even if there were good intentions at first, not that much in jQuery really lends to structuring the application in any particular way. AngularJS in turn at least has the built in Controllers and Services to help separate concerns. That’s the biggest difference in my experience - Angular apps feel somewhat more maintainable when the amount of code increases past trivial.

I don’t have any particular suggestions for replacements of jQuery features; generally you should just use the idiomatic Angular way to do things. Definitely don’t use jQuery and Angular on the same page if you can at all avoid it.

I don’t think server-side comes to play that much - you just call some REST services and do stuff with the results.