Due to the rapid development of wireless access technologies and smart terminals, mobile data traffic is continuously increasing, which is expected to lead to an explosive growth of data in heterogeneous networks especially cellular networks. It is significant for network operators to expand the capacity of cellular networks to avoid congestion and overload so as to guarantee users’ satisfaction. Given that contemporary terminals are capable of both WiFi and cellular networks, WiFi offloading is envisioned as a promising solution to utilize the various benefits of WiFi and cellular networks to migrate traffic from cellular networks to WiFi networks. This paper surveys the state-of-the-art progress in the field of WiFi offloading. After discussing the requirements from the emerging 5G technology regarding the coexistence of WiFi and cellular networks, selecting and switching schemes are presented. The bandwidth and capacity of WiFi networks are usually excellent, whereas the coverage and energy efficiency may be unacceptable. We elaborate on several existing solutions of WiFi offloading schemes and discuss how the parameters of several kinds of heterogeneous networks affect the offloading decision. We also illustrate how multiple networks cooperate in heterogeneous networks in order to balance the offloading performance. We classify current various incentives of WiFi offloading into five categories: 1) capacity; 2) cost; 3) energy; 4) rate; and 5) continuity. Improving the capacity is the basic incentive, which can be further classified in terms of delay techniques. From operators’ and users’ perspectives, we also investigate various state-of-the-art incentives of WiFi offloading such as minimizing cost, saving energy consumption, and improving rate. Furthermore, WiFi offloading schemes that attempt to enhance continuity to deal with frequent disruption problems are further investigated, especially for vehicular scenarios. Finally, future research directions and challenges for WiFi offloading strategies are presented in various incentives of WiFi offloading.