In recent years, the growth the in the number of heterogeneous interconnected systems, as well as the emergence of new requirements in applications and services are progressively changing the original simplicity and transparency of the Internet architecture. When this architecture was designed, the main goal was to interconnect stationary host. Therefore, the appearance of mobile communications has made necessary to adapt traditional protocols in order to accommodate mobile users. This implies a new interaction between the mobile network and the fixed access network. This paper describes the main IP mobility protocols both centralized and distributed paradigms, and emergent approaches based on software defined networking. Moreover, a novel classification is presented, which relates the integration of the mobility protocol with the access network. Analytical models evaluate the registration updates cost and the packet loss rate of the classified protocols.