Graphene quantum dots (GQDs) are a new class of fluorescent reporters promising various novel applications including bio-imaging, optical sensing and photovoltaics. They have recently attracted enormous interest owing to their extraordinary and tunable optical, electrical, chemical and structural properties. The widespread use of GQDs, however, is hindered by the current poor understanding of their photoluminescence (PL) mechanisms. Using density-functional theory (DFT) and time-dependent DFT calculations, we reveal that the PL of a GQD can be sensitively tuned by its size, edge configuration, shape, attached chemical functionalities, heteroatom doping and defects. In addition, it is discovered that the PL of a large GQD consisting of heterogeneously hybridized carbon network is essentially determined by the embedded small sp2 clusters isolated by sp3 carbons. This study not only provides explanation to the previous experimental observations but also provides insightful guidance to develop methods for controllable synthesis and engineering of GQDs.