Compiz is a compositing window manager that is now the default in Ubuntu's Unity desktop environment.
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Cube desktop is appealing to some users, in addition to many of the other visual effects Compiz can manage.
Compiz has plug-ins that can be enabled / disabled in order to alter its behavior.
Pro Has great wobbly windows
Pro Unity Shell
Unity Shell is a plug-in available for Compiz and so is needed for Unity to exist. Unity is also the default desktop environment for Ubuntu and is arguably the most popular Linux distro to date.
Con Heavy window manager
Compiz is one of the heavier window managers around: it uses higher amounts of RAM and CPU than other options
Con Requires 3D acceleration
If this is not present in the system, it will offload from the GPU to the CPU.
Con Crashes frequently
Breaks in the system are frequent.