The widespread proliferation of handheld devices enables mobile carriers to be connected at anytime and anywhere. Meanwhile, the mobility patterns of mobile devices strongly depend on the users' movements, which are closely related to their social relationships and behaviors. Consequently, today's mobile networks are becoming increasingly human centric. This leads to the emergence of a new field which we call socially-aware networking (SAN). One of the major features of SAN is that social awareness becomes indispensable information for the design of networking solutions. This emerging paradigm is applicable to various types of networks (e.g. opportunistic networks, mobile social networks, delay tolerant networks, ad hoc networks, etc) where the users have social relationships and interactions. By exploiting social properties of nodes, SAN can provide better networking support to innovative applications and services. In addition, it facilitates the convergence of human society and cyber physical systems. In this paper, for the first time, to the best of our knowledge, we present a survey of this emerging field. Basic concepts of SAN are introduced. We intend to generalize the widely-used social properties in this regard. The state-of-the-art research on SAN is reviewed with focus on three aspects: routing and forwarding, incentive mechanisms and data dissemination. Some important open issues with respect to mobile social sensing and learning, privacy, node selfishness and scalability are discussed.