A remarkable property of one-dimensional all-dielectric periodic structures has recently been reported, namely a one-dimensional lattice can totally reflect electromagnetic wave of any polarization at all angles within a prescribed frequency region. Unlike their metallic counterpart, such all-dielectric omnidirectional mirrors are nearly free of loss at optical frequencies. Here we discuss the physics, design criteria and applications of the thin-film all-dielectric omnidirectional mirror. The experimental demonstration of the mirror is presented at optical frequencies.