Live virtual machine migration is a valuable feature for the virtualized data center or cloud environment. This is the process to migrate running virtual machines from one physical host to another host. Live virtual machine migration can be used to provide various benefits such as server consolidation, energy-saving, and maintenance. It is a valuable feature for the virtualized data center or cloud environment. Cloud computing provides IT capabilities as a service and its key technology is virtualization. The key benefit of virtualization is to offer better resource employment by executing various VMs on the same physical system. In this research, we analyze the performance of the various hypervisors based on their migration features and compares the migration feature. Hypervisors are Xen, VMWare, KVM, and their migration feature are XenMotion, vMotion, and KVM migration, respectively. According to our study, we find that there are many factors that affect the performance of the live virtual machine migration such as a long downtime, the large amount of data that is sent in an iteration manner so with a higher dirtying rate the total migration time extends. In our comparison, we show VMWare has the least downtime.  We also identify and discuss the various research challenges in detail to stimulate the researchers to work in this direction.