Graphene has many novel optical and electrical properties desirable for applications in future electrooptical devices. Graphene nanostructures are especially attractive for their wide range of tunable properties. Here we describe the recent progress and challenges in the solution-chemistry approach to graphene nanostructures. This approach could not only lead to new materials with various well-defined properties, but also enable their production in large quantities.Graphene, containing a single layer of sp 2 -hybridized carbon atoms, has become an intensively studied topic because of its unique two-dimensional (2D) crystalline structure, extraordinary physical properties, 1-3 and potential applications in future optics and electronics. Even though graphene is the basic building block for graphite, carbon nanotubes, and fullerenes which have been studied for decades, not a lot of attention was paid to graphene until the first isolation of single-layer graphene from graphite by Geim and his co-workers 4 with a ''Scotch tape'' approach in 2004. Numerous follow-up investigations subsequently revealed a wide range of very attractive properties, such as extremely high carrier mobilities, 5-9 quantum hall effect, 10-16 and ambipolar field effect, 4,17 etc. These properties make graphene a very promising material for future devices, such as high-speed, high-frequency electronic devices, 6,7,18-21 single molecule sensors, 22,23 and ultrathin transparent electrodes. [24][25][26][27][28][29][30][31] Reliable production of graphene with high quality and in large quantities is still a challenge. 32 Although some proof-of-concept devices have been made from mechanically exfoliated graphene, the original layer-by-layer peel-off method cannot be used for large-scale production. In order to overcome this challenge, two distinct approaches have been taken by scientists: breaking down graphite into graphene (''top-down'' approach) and building up graphene from atomic or molecular building blocks (''bottom-up'' approach). The top-down approaches include mechanical exfoliation, 1,4,18 intercalation followed by solution-based exfoliation, 28,30,33-45 reduction of graphene oxide, 46-56 etc, (Fig. 1). The bottom-up approaches mostly include chemical vapor deposition (CVD) 31,57-66 and a solution-chemistry approach. 67,68 In this review we discuss the latest development in the emerging solution-chemistry approach to graphene nanostructures, especially quantum dots (QDs). 69 We refer readers to some recent reviews 70-72 for detailed descriptions of top-down approaches and CVD methods to make graphene.To make stable single-layer graphene it is essential to overcome inter-layer van der Waals attraction that favors formation of graphite. It is achieved in mechanical exfoliation with external forces, and in CVD methods with introduction of substrates to simultaneously immobilize graphene when they form.