Two classes of carbon nanomaterials—carbon nanotubes and graphene—have promoted the advancement of nanoelectronics, quantum computing, chemical sensing and storage, thermal management, and optoelectronic components. Studies of the thermal radiative properties of carbon nanotube thin film arrays and simple graphene hybrid structures reveal some of the most exciting characteristic electromagnetic interactions of an unusual sort of material, called hyperbolic metamaterials. The features and results on these materials in the context of both far-field and near-field radiation are presented in this dissertation. Due to the optically dark nature of pyrolytic carbon in the wavelength range from visible to infrared, it has been suggested vertically aligned carbon nanotube (VACNT) coatings may serve as effective radiative absorbers. The spectral optical constants of VACNT are modeled using the effective medium theory (EMT), which is based on the anisotropic permittivity components of graphite. The effects of other EMT parameters such as volume filling ratio and local filament alignment factor are explored. Low reflectance and high absorptance are observed up to the far-infrared and wide range of oblique incidence angles. The radiative properties of tilt-aligned carbon nanotube (TACNT) thin films are illustrated. Energy streamlines by tracing the Poynting vectors are used to show a self-collimation effect within the TACNT thin films, meaning infrared light can be transmitted along the axes of CNT filaments. Graphene, a single layer sheet of carbon atoms, produces variable conductance in the terahertz frequency regime by tailoring the applied voltage gating or doping. Periodically embedding between dielectric spacers, the substitution of graphene provides low radiative attenuation compared to traditional metal-dielectric multilayers. The hyperbolic nature, namely negative angle of refraction, is tested on the graphene-dielectric multilayers imposed with varying levels of doping. EMT should be valid for graphene-dielectric multilayers due to the nanometers-thick layers compared to the characteristic wavelength of infrared light. For metal- or semiconductor-dielectric multilayers with thicker or lossier layers, EMT may not hold. The validity of EMT for these multilayers is better understood by comparing against the radiative properties determined by layered medium optics. When bodies of different temperatures are separated by a nanometers-size vacuum gap, thermal radiation is enhanced several-fold over that of blackbodies. This phenomenon can be used to develop more efficient thermophotovoltaic devices. Due to their hyperbolic nature, VACNT and graphite are demonstrated to further increase evanescent wave tunneling. The heat flux between these materials separated by vacuum gaps smaller than a micron is vastly improved over traditional semiconductor materials. A hybrid structure composed of VACNT substrates covered by doped graphene is analyzed and is shown to further improve the heat flux, due to the surface plasmon polariton coupling between the graphene sheets.