What's with the branch instructions "Branch with Link" and "Branch with Exchange"?

What do they do? I haven't seen anything like this before.

I see some explanation in https://azeria-labs.com/arm-conditional-execution-and-branch... but the reason why branching must work this way isn't explained.

edit: I see "Branch with Exchange" switches the processor from ARM to Thumb in http://www.embedded.com/electronics-blogs/beginner-s-corner/.... But I don't see why switching processor modes must happen on branch instructions.