How do authors deal with figure copyrights when writing review articles? Assuming I'm writing a review article and I'd like to use figures 
after [1]" or similar? How am I expected to deal with copyright?  Obviously a review article is going to use existing figures, more or less--that's the point.  It seems from sites like IEEE that the expected practice is to pay, per figure, for each graphic used.  Is that really how things work?  Or is there some "fair use" clause that can be invoked?
The rules vary widely by publisher here. It also depends on whose work you're "copying." If it's your own graphic, then there's usually no issue associated with it. However, if it belongs to someone else, then you should either request the permission from the rights holder, or redraw the figure yourself (if it's a schematic, then this would eliminate copyright issues).

Similarly, a journal or publisher may allow you to reuse people's work from within the same publisher's journals without fee. But again, this is something the individual publishers determine.