The across-the-global diffusion of smartphones is initiating an enormous growth of data traffic. Soon, the existing cellular networks will suffer from traffic overload issues, and establishing additional infrastructure might be the costlier solution. An offloading of the traffic to different networks is considered a promising approach. Opportunistic offloading refers to diverting traffic from a cellular network to Opportunistic Networks (OppNets) by utilizing nearby devices having idle computing resources through opportunistic contacts. As a case study, we analyzed the number of sensors needed and the amount of data generated in Ahmedabad and Gandhinagar by considering the smart city scenario. The paper comprehensively reviews OppNets in data offloading for various scenarios and applications of smart cities. We further point out the important future challenges, problems, and applications.