This chapter deals with the modeling and design of inner resonance media, i.e. media that present a local resonance which has an impact on the overall dynamic behaviour. The aim of this chapter is to provide a synthetic picture of the inner resonance phenomena by means of the asymptotic homogenization method (Sanchez-Palencia, 1980). The analysis is based on the comparative study of a few canonical realistic composite media. This approach discloses the common principle and the specific features of different inner resonance situations and points out their consequences on the effective behavior. Some general design rules enabling to reach such a specific dynamic regime with a desired effect are also highlighted. The paper successively addresses different materials  having different behaviours and inner structures as elastic composites, reticulated media, permeable rigid and elastic media,  undergoing phenomena governed either by momentum transfer or/and mass transfer,  in which the inner resonance mechanisms can be highly or weakly dissipative,  in situation of inner resonance or inner anti-resonance.