Cyber-Physical convergence, the fast expansion of the Internet at its edge, and tighter interactions between human users and their personal mobile devices push toward an Internet where the human user becomes more central than ever, and where their personal devices become their proxies in the cyber world, in addition to acting as a fundamental tool to sense the physical world. The current Internet paradigm, which is infrastructure-centric, is not the right one to cope with such emerging scenario with a wider range of applications. This calls for a radically new Internet paradigm, that we name the Internet of People (IoP), where the humans and their personal devices are not seen merely as end users of applications, but become active elements of the Internet. Note that IoP is not a replacement of the current Internet infrastructure, but it exploits legacy Internet services as (reliable) primitives to achieve end-to-end connectivity on a global-scale. In this visionary paper, we first discuss the key features of the IoP paradigm along with the underlying research issues and challenges. Then we present emerging networking and computing paradigms that are anticipating IoP.