Electrons and positrons channeled in crystals traverse periodic trajectories which, as in an undulator, results in the emission of narrow band electromagnetic radiation. This radiation can cover the soft x-ray to y-ray portion of the spectrum, with the photon energy dependent upon the particle energy. In silicon, for example, with y = 100 where y is the ratio of the particle energy to its rest energy, forward-directed photon energies from planar-channeled particles are in the 20 - 130 keV range. The potential function for positrons trapped between crystal planes is nearly harmonic, so that the eigenvalues derived from this potential are approximately equally spaced and therefore result in a single emission frequency. Electrons are in a potential with an approximate exponential dependence upon coordinate, yielding multiple emission frequencies. Emission linewidths (full-width, half-maximum) have been predicted and measured to be in the 10 - 25% range. The important factors contributing to this linewidth are the finite coherence length for radiation, particle beam divergence, potential anharmonicity (for the case of positrons), energy spread of the particles, finite crystal thickness, and broadening associated with crystal periodicity (Bloch-wave broadening). For relativistic particles the emission is within a cone in the forward direction with half-angle y-1. The radiation is linearly polarized, and has an intensity that is up to an order of magnitude larger than bremsstrahlung for a randomly directed particle. The time structure of the radiation reproduces the time structure of the particle beam which, for our linear accelerator, is composed of 10 picosecond bursts.