Cloud computing is a technology which relies on sharing various computing resources instead of having local servers to handle applications. Cloud computing is driven by virtualization technology. Virtual machines need migration from one host to anther due to the presence of error or over loading or slowness in the current running host machine. Live Virtual machine migration is the transfer of running virtual machine from one host to another without stopping the current running task. During this live virtual machine migration Downtime is one of the key factors that have to be considered and assessed. Here we present detailed survey on what are the importance of live virtual machine migration in cloud computing technology and various techniques to reduce the downtime during live virtual machine migration. The flow chart showing the steps used in Pre copy approach for VM migration. And also we present the result of the comparison between the two virtual machine migration environments, VMWare and Xen Server.