How do I move around and otherwise rearrange splits in vim?

Problem

So far, I've figured out swapping splits laterally via , and that's pretty much it. How do I move a split anywhere in a viewport that contains multiple vertical and horizontal splits? How do I create a horizontal split that, say, spans the entire top half of the screen after I have already opened a few vertical splits? (Currently, when I create a new horizontal split in an already-vertically-split viewport, I get a horizontal split in one of the columns.) Perhaps most vim users prefer tabs over splits, but I really like the latter because I work on a 30" monitor! :-)