The Next Generation Wireless Systems (NGWSs) consists of heterogeneous wireless access networks such as UMTS, Wi-Fi, WiMAX and LTE where Mobile Users (MUs) can access these technologies and services using a single device. This device is equipped with multiple radio interfaces include devices capable of supporting multiple Radio Access Technologies (RATs) by incorporating several interface cards and appropriate software for switching between multiple access systems (Vertical Handover (VHO)). The Access Network Selection (ANS) regarding the transferring between different RATs is based on network conditions, mobile conditions, user preferences, Quality of Service (QoS) requirements and service cost. This paper overviews VHO approaches proposed in the literature and classify them into three categories based on ANS methods for which their characteristics are presented. Finally, a conclusion about who is a dominant ANS method for seamless VHO is given.