Due to the rapid evolution of Internet as well as services over the Internet, including high bandwidth consuming applications like audio and video streaming, it has become need of the day to enhance the Internet infrastructure for bandwidth efficiency. Developed by the Internet Engineering Task Force, MPLS allows networks to offer several services on the single network architecture with improved forwarding speed of routers by solving problem of longest prefix match in IP networks. In addition to this, it offers Traffic Engineering, Virtual Private Networks and Quality of Service guarantees. MPLS in combination with Internet Protocol version 6 (IPv6) has been seen as a technology for next generation Internet, which can revolutionize the Internet with speed, services and functionality. IPv6 provides huge number of addresses and guaranteed support for the ever increasing demand. However, there is a disadvantage of bigger packet header size compared to the payload size which leads to excessive overhead in case of real-time multimedia applications. Bandwidth can be conserved by reducing the amount of redundant IP header transmitted with every packet for the same packet stream through header compression/suppression techniques. The objective of this paper is to survey of various header compression technologies which can be implemented over MPLS with IPv6 as the addressing protocol, which can be used as a bandwidth conserving technology. The current efforts in the area, both standardised as well as ongoing research has been discussed in detail and also the problems that are yet to be addressed are examined.