We present a research roadmap of a Planetary Nervous System (PNS), capable of sensing and mining the digital breadcrumbs of human activities and unveiling the knowledge hidden in the big data for addressing the big questions about social complexity. We envision the PNS as a globally distributed, self-organizing, techno-social system for answering analytical questions about the status of world-wide society, based on three pillars: social sensing, social mining, and the idea of trust networks and privacy-aware social mining. We discuss the ingredients of a science and a technology necessary to build the PNS upon the three mentioned pillars, beyond the limitations of their respective state-of-art. Social sensing is aimed at developing better methods for harvesting the big data from the techno-social ecosystem and make them available for mining, learning and analysis at a properly high abstraction level.Social mining is the problem of discovering patterns and models of human behaviour from the sensed data across the various social dimensions by data mining, machine learning and social network analysis. Trusted networks and privacy-aware social mining is aimed at creating a new deal around the questions of privacy and data ownership empowering individual persons with full awareness and control on own personal data, so that users may allow access and use of their data for their own good and the common good. The PNS will provide a goal-oriented knowledge discovery framework, made of technology and people, able to configure itself to the aim of answering questions about the pulse of global society. Given an analytical request, the PNS activates a process composed by a variety of interconnected tasks exploiting the social sensing and mining methods within the transparent ecosystem provided by the trusted network.