The development of mobile Internet and wireless communication technologies promote heterogeneous wireless networks (HWNs), in which a variety of wireless networks coexist and coverage overlap. The differences between various wireless access technologies and single network cannot meet all the requirements of users. Consequently, it is inevitable for the integration of HWNs. The access selection as one of the key technologies of HWNs has become a research hotspot. Based on analyzing the infrastructure of HWNs and the concepts of the access selection, this paper focuses on the classification and detailed comparative analysis of the access selection algorithm. Simultaneously, the existent problems are summarized, and the future research directions and challenges are presented.