We investigate localized and resonant optical waves associated with a semiinfinite one-dimensional photonic crystal constructed by two different layers (1 and 2) and terminated with a cap layer. In this chapter, we present an analytic determination of the response function (Green's function) for a semiinfinite superlattice with or without a cap layer, and for a photonic crystal in contact with a substrate. Both transverse electric and transverse magnetic waves are considered. These surface modes are analogous to the so-called Tamm states associated with electronic states found at the surface of periodic materials. The surface guided modes induced by the cap layer strongly depend on whether the photonic crystal ends with a material 1 or 2, the thickness of the surface layer, as well as on the polarization of the waves. Different periodic structures are considered, such as dielectric\textendash dielectric, dielectric\textendash superconductor, and semiconductor\textendash semiconductor photonic crystals. Different kinds of surface modes are found and their properties examined. In the case where one of the layers is a superconductor medium, the surface mode depends also on the temperature of the superconductor layer. This last structure can be used to realize highly sensitive photonic crystal sensors.