Not for the first time, I found myself the other night explaining on IRC how the window manager and window decorator parts fit together. There seems to be a misconception that Compiz requires Emerald. That is far from true. There also seems to be confusion regarding what different kinds of themes do. So let's start at the basics.
The three most common window managers in the Ubuntu world are Metacity, Compiz, and Kwin. Yes, there are others, such as Enlightenment, Fluxbox, Xmonad, and Ion, but I'm not going to go into why each of them rocks. Metacity is the default GNOME window manager. Kwin is the KDE window manager. And then there's Compiz. Compiz is the compositing window manager that is enabled in Ubuntu by default if your system can handle it. The function of the window manager is to draw the windows in a certain place, with a certain size, and let them be movable and resizable.
Then you have the window decorator. This is where people get tripped up. The window decorator draws the window borders. It is not necessary to move the window, since alt+click&drag will still work even when the window decorator has crashed. I think the confusion comes from the fact that Kwin and Metacity have their decorators built in. Xmonad doesn't decorate windows at all. Compiz is a bit more modular in this regard. It has always been able to use Metacity's themes for the window borders. The window decorator in use when doing this is gtk-window-decorator. It can also use Kwin's themes, in which case you're using kde-window-decorator.
And then there's Emerald. Emerald was the window decorator for Beryl. Beryl merged back with Compiz a bit over a year ago. I remember Quinnstorm telling me she hopes "eventually to totally rewrite emerald," but that hasn't happened. Well, earlier this year, after noticing some glitches with my friend's Nvidia card and Emerald, I asked in #compiz-fusion and they said to stop using Emerald because it's not really being developed anymore and they'd rather everyone just switch to either gtk-window-decorator or kde-window-decorator. They did say that they were considering writing a replacement for Emerald, but that hasn't happened either. MOTU tried removing Emerald, I'm guessing due to its issues, but apparently a lot of people complained because they'd rather have a window decorator that crashes 3 times a day.
And now the last bit about themes. I said before that Compiz can use Kwin and Metacity's themes just fine thanks to kde-window-decorator and gtk-window-decorator. Some people are confused about what exactly comprises a Metacity theme versus a GTK theme, especially since they are installed in the same place. A GTK theme controls how buttons look, the colors of text, the window background, the scrollbars, and the menubar styles. The Metacity theme just controls the window border's style. For KDE, the Qt theme does the buttons, scrollbars, etc., and Kwin has its own themes for window borders, I think.