With the name “phenine” given to 1,3,5-trisubstituted benzene for a fundamental trigonal planar unit to weave nanometer-sized networks, a series of curved nanocarbon molecules have been designed and synthesized. Since the 6π-phenine units were amenable to modern biaryl coupling reactions mediated by transition metals, concise syntheses of >400π-nanocarbon molecules were readily achieved. In addition, the phenine design allowed for installing of heteroatoms and/or transition metals doped at specific positions of the large π-systems of the nanocarbon molecules. Fundamental tools were also developed to specify and describe the locations of defects/dopants, quantify pyramidalizations of trigonal panels and estimate molecular Gauss curvatures of the discrete surface. Unique features of phenine nanocarbons, such as stereoisomerism, entropy-driven molecular assembly and effects of dopants on electronic/magnetic characteristics, were revealed during the first half-decade of investigations.