Graphene is a 2-D atomic layer of carbon atoms with unique electronic transport properties such as a high Fermi velocity, an outstanding carrier mobility, and a high carrier saturation velocity, which make graphene an excellent candidate for advanced applications in future electronics. In particular, the potential of graphene in high-speed analog electronics is currently being extensively explored. In this paper, we discuss briefly the basic electronic structure and transport properties of graphene, its large scale synthesis, the role of metal-graphene contact, field-effect transistor (FET) device fabrication (including the issues of gate insulators), and then focus on the electrical characteristics and promise of high-frequency graphene transistors with record-high cutoff frequencies, maximum oscillation frequencies, and voltage gain. Finally, we briefly discuss the first graphene integrated circuits (ICs) in the form of mixers and voltage amplifiers.