We study the dielectric annular billiard as a quantum chaotic model of a micro-optical resonator. It differs from conventional billiards with hard-wall boundary conditions in that it is partially open and composed of two dielectric media with different refractive indices. The interplay of reflection and transmission at the different interfaces gives rise to rich dynamics of classical light rays and to a variety of wave phenomena. We study the ray propagation in terms of Poincare surfaces of section and complement it with full numerical solutions of the corresponding wave equations. We introduce and develop an S-matrix approach to open optical cavities which proves very suitable for the identification of resonances of intermediate width that will be most important in future applications like optical communication devices. We show that the Husimi representation is a useful tool in characterizing resonances and establish the ray-wave correspondence in real and phase space. While the simple ray picture provides a good qualitative description of certain system classes, only the wave description reveals the quantitative details.