IP multicast is a technique for one-to-many and many-to-many communication over an IP infrastructure in a network. It provides an efficient and cost effective way to accommodate requirements of various applications like Internet TV, Video on Demand, etc. Many protocols support efficient multicast by using a multicast delivery tree. The main drawback of these protocols is that they are designed to support the multicast parties whose members are stationary. The movement of multicast member causes in reality many problems to multicast service. The Internet Engineering Task Force (IETF) proposed the Mobile IPv6 (MIPv6) protocol, the Proxy Mobile IPv6 (PMIPv6) protocol and many solutions that are based on these protocols to solve these problems. In this document, we would like to generally introduce the problems and solutions to deploy multicast service with to 2 approaches: centralized mobility approach and distributed mobility approach.