The recent developments in networking research leverage the principles of virtualization and service-orientation to enable fundamental changes in network architecture, which forms a trend of network cloudification that enables network systems to be realized using cloud technologies and network services to be provisioned following the cloud service model. On the other hand, the latest progress in cloud and fog computing has made networking an indispensable ingredient for cloud/fog service delivery. Convergence of networking and cloud/fog computing technologies enables unification of network and cloud/fog service provisioning, which has become an active research area that attracts interest from both academia and industry. In this paper, we introduce the notion of network-cloud/fog service unification and propose an architectural framework for unified network-cloud/fog service provisioning. Then we present a survey that reflects the state of the art of research on enabling network-cloud/fog service unification. We also discuss challenges to realizing such unification and identify some opportunities for future research, with a hope to arouse the research community's interest in this exciting interdisciplinary field.