I studied the optical properties of two kinds of chiral photonic crystal, the spiral photonic crystal and the chiral woodpile photonic crystal. Both of these photonic crystals process a frequency regime in which only one of the circular polarizations of light is allowed to propagate in them. This frequency regime is known as the polarization gap, and inside the polarization gap, Fabry-Perot effect is suppressed. This thesis discusses the physics behind this suppression. The polarization gap modifies the density of states for one of the circular polarizations, and the thermal radiation spectrum resulting from this modification is also discussed. I demonstrate that the thermal radiation from a dielectric chiral photonic crystal can be almost circularly polarized. The thermal radiation from a metallic chiral woodpile photonic crystal is also discussed. Some of the features in the thermal radiation spectrum from this kind of photonic crystal come from the coupled plasmon modes of the individual layers of rods. I also demonstrate that placing a metal plate underneath the photonic crystal results in emission peaks that come from magnetic resonance. In addition to applications in thermal radiation, the application of a chiral photonic crystal in negative refraction is discussed.