A negative index material (NIM), which possesses simultaneously negative permittivity and permeability, is an emerging material that has caught many researchers attention after it was first demonstrated in 2001. It has been shown that electromagnetic waves propagating in NIMs have some remarkable properties such as negative phase velocities and negative refraction and hold enormous promise for applications in imaging and optical communications. This dissertation is centered on investigating the unique aspects of the radiative properties of NIMs. Photon tunneling, which relies on evanescent waves to transfer radiative energy, has important applications in thin-film structures, microscale thermophotovoltaic devices, and scanning thermal microscopes. With multilayer thin-film structures, photon tunneling is shown to be greatly enhanced using NIM layers. The enhancement is attributed to the excitation of surface or bulk polaritons, and depends on the thicknesses of the NIM layers according to the phase matching condition. A new coherent thermal emission source is proposed by pairing a negative permittivity (but positive permeability) layer with a negative permeability (but positive permittivity) layer. The merits of such a coherent thermal emission source are that coherent thermal emission occurs for both s- and p-polarizations, without use of grating structures. Zero power reflectance from an NIM for both polarizations indicates the existence of the Brewster angles for both polarizations under certain conditions. The criteria for the Brewster angle are determined analytically and presented in a regime map. The findings on the unique radiative properties of NIMs may help develop advanced energy conversion devices. Motivated by the recent advancement in scanning probe microscopy, the last part of this dissertation focuses on prediction of the radiation heat transfer between two closely spaced semi-infinite media. The objective is to investigate the dopant concentration of silicon on the near-field radiation heat transfer. It is found that the radiative energy flux can be significantly augmented by using heavily doped silicon for the two media separated at nanometric distances. Large enhancement of radiation heat transfer at the nanoscale may have an impact on the development of near-field thermal probing and nanomanufacturing techniques.