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Graphene has promised many novel applications in nanoscale electronics and sustainable energy due to its novel electronic properties. Computational exploration of electronic functionality and how it varies with architecture and doping presently runs ahead of experimental synthesis yet provides insights into types of structures that may prove profitable for targeted experimental synthesis and characterization. We present here a summary of our understanding on the important aspects of dimension, band gap, defect, and interfacial engineering of graphene based on state-of-the-art ab initio approaches. Some most recent experimental achievements relevant for future theoretical exploration are also covered.