Over the last decade or so, the study of complex networks has attracted a surge of interest in varied branches of science and industry, from engineering to economics, from neurobiology to statistical physics. Network theory emerging as a blooming science has been recognized as a network-based paradigm that is taking science by storm. Much progress has been achieved, but even more questions are being posed. At the dawn of the millennium, S.H.Strogatz enumerated some possible complications facing network theory: (1) structural complexity; (2) network evolution; (3) connection diversity; (4) dynamical complexity; (5) node diversity; and (6) meta-complication. These challenges have resisted complete solutions so far. A special issue on complex systems and networks composed by leading scientists in the field was honored by Science in 2009, which highlights important sweeping advances as well as up-to-date insightful perspectives. Albeit young, network theory was preceded by an old and profound subject, graph theory, in mathematics that governs the discrete universe.