Graphene is a material with outstanding properties that make it an excellent candidate for advanced applications in future electronics and photonics. The potential of graphene in high-speed analog electronics is currently being explored extensively because of its high carrier mobility, its high carrier saturation velocity, and the insensitivity of its electrical-transport behavior to temperature variations. Herein, we review some of the key material and carrier-transport physics of graphene, then focus on high-frequency graphene field-effect transistors, and finally discuss graphene monolithically integrated circuits (ICs). These high-frequency graphene transistors and ICs could become essential elements in the blossoming fields of wireless communications, sensing, and imaging. After discussing graphene electronics, we describe the impressive photonic properties of graphene. Graphene interacts strongly with light over a very wide spectral range from microwaves to ultraviolet radiation. Most importantly, the light–graphene interaction can be adjusted using an electric field or chemical dopant, making graphene-based photonic devices tunable. Single-particle interband transitions lead to a universal optical absorption of about 2% per layer, whereas intraband free-carrier transitions dominate in the microwave and terahertz wavelength range. The tunable plasmonic absorption of patterned graphene adds yet another dimension to graphene photonics. We show that these unique photonic properties of graphene over a broad wavelength range make it promising for many photonic applications such as fast photodetectors, optical modulators, far-infrared filters, polarizers, and electromagnetic wave shields. These graphene photonic devices could find various applications in optical communications, infrared imaging, and national security.