An overview of the different technologies in Linux virtualization.
The original x86 architecture is not virtualizable, because some instructions behave differently depending on whether or not the CPU is running in privileged mode. Because a guest virtual machine does not run in privileged mode (for obvious security reasons), pure software full virtualization software like vmware or qemu deals with these instructions by replacing them with other instructions on the fly.
This instruction rewriting can be quite expensive. If the guest operating system kernel would simply never call the unvirtualizable instructions, that overhead could be avoided. While we're changing the guest operating system anyway, why not stop pretending we are emulating real hardware, and give it lower overhead virtual devices instead?
In a nutshell, this is paravirtualization. In order to run more efficiently, the guest operating system's kernel is changed out for a kernel that behaves well in a virtualized environment.
Xen, lhype and User Mode Linux do paravirtualization on x86. IBM POWER also does something along the same lines, with the hypervisor taking care of pagetable updates.
Hardware assisted virtualization
Intel VT and AMD-V capable CPUs can run all instructions in an unprivileged virtual machine, and have them behave well. However, when running an unmodified operating system, many operations simply trap to the hypervisor and still need to be emulated. However, it allows for a much cleaner implementation of full virtualization.
Xen and KVM do hardware assisted full virtualization.
Coopvirt (cooperative virtualization) is an interesting hybrid between paravirtualization and hardware assisted full virtualization. The idea is to use the hardware capabilities of Intel VT and AMD-V to do some of the virtualization that is done in software by paravirtualization, while still having a well behaved guest that can run very efficiently in a virtualized environment.
As of late 2006, coopvirt on x86 is still in a research and prototyping phase. However IBM mainframes have been using something along the lines of coopvirt for decades.