Virtualization techniques effectively handle the growing demand for computing, storage, and communication resources in large-scale Cloud Data Centers (CDC). It helps to achieve different resource management objectives like load balancing, online system maintenance, proactive fault tolerance, power management, and resource sharing through Virtual Machine (VM) migration. VM migration is a resource-intensive procedure as VM's continuously demand appropriate CPU cycles, cache memory, memory capacity, and communication bandwidth. Therefore, this process degrades the performance of running applications and adversely affects efficiency of the data centers, particularly when Service Level Agreements (SLA) and critical business objectives are to be met. Live VM migration is frequently used because it allows the availability of application service, while migration is performed. In this paper, we make an exhaustive survey of the literature on live VM migration and analyze the various proposed mechanisms. We first classify the types of Live VM migration (single, multiple and hybrid). Next, we categorize VM migration techniques based on duplication mechanisms (replication, de-duplication, redundancy, and compression) and awareness of context (dependency, soft page, dirty page, and page fault) and evaluate the various Live VM migration techniques. We discuss various performance metrics like application service downtime, total migration time and amount of data transferred. CPU, memory and storage data is transferred during the process of VM migration and we identify the category of data that needs to be transferred in each case. We present a brief discussion on security threats in live VM migration and categories them in three different classes (control plane, data plane, and migration module). We also explain the security requirements and existing solutions to mitigate possible attacks. Specific gaps are identified and the research challenges in improving the performance of live VM migration are highlighted. The significance of this work is that it presents the background of live VM migration techniques and an in depth review which will be helpful for cloud professionals and researchers to further explore the challenges and provide optimal solutions.