Mobility IP protocols are intended to ensure that mobile nodes remain reachable while traversing the Internet. There are two primary approaches to mobility management: host-based and network-based. Mobile IPv6 (MIPv6), a host-centric mobility management protocol, stands out as a significant initiative proposed by the Internet Engineering Task Force (IETF) to serve as the main protocol for mobility management at the IP layer. To address the shortcomings of the host-based MIPv6 protocol, including issues such as suboptimal routing, delivery delays, packet loss, and the risk of a single point of failure, the IETF has standardized the Proxy Mobile IPv6 (PMIPv6) protocol. This document outlines the fundamental specifications of PMIPv6 and examines various extensions that has been proposed by standardization organizations and researchers to enhance the core PMIPv6 protocol. These enhancements aim to provide a more comprehensive mobility experience, incorporating features such as aggregation, rapid delivery, path optimization, support for network mobility, and load balancing. The research conducted on these extensions is evaluated to pinpoint critical considerations that should be taken into account during their design.