The connected and autonomous vehicles   (CAV)   applications and services-based traffic make an extra burden on the already congested cellular networks. Offloading is envisioned as a promising solution to tackle cellular networks’  traffic explosion problem. Notably, vehicular traffic offloading leveraging different vehicular communication network (VCN) modes is one of the potential techniques to address the data traffic problem in cellular networks. This paper surveys the state-of-the-art literature for vehicular data offloading under a communication perspective,  i.e.,  vehicle to vehicle  (V2V),  vehicle to roadside infrastructure  (V2I),  and vehicle to everything  (V2X). First, we pinpoint the significant classification of vehicular data/traffic offloading techniques, considering whether data is to download or upload. Next, for better intuition of each data offloading’s category,  we sub-classify the existing schemes based on their objectives. Then, the existing literature on vehicular data/traffic is elaborated, compared, and analyzed based on approaches, objectives, merits, demerits, etc. Finally, we highlight the open research challenges in this field and predict future research trends.