Due to high surface-to-volume ratio and quantum confinement, nanoscale structures have special properties, which are dramatically different from their macroscopic version. For graphene nanostructures, surfaces and edges strongly govern their electronic, magnetic and chemical properties. I will discuss our scanning tunneling microscopy (STM) and spectroscopy (STS) explorations of a quasi-one-dimensional graphene nanostructure, graphene nanoribbons, where size quantization and electron-electron interactions induce novel magneto-electronic behaviors. Our results provide compelling evidence for theoretically predicted edge states and a size-tunable energy gap of chiral graphene nanoribbons, both of which are crucial for potential applications of graphene in nanoelectronics, photovoltaics and spintronics.