The main radiation and scattering properties of cavity backed microstrip patch antennas loaded by homogeneous and inhomogeneous chiral, ferromagnetic and bianisotropic materials are investigated in this paper. The theoretical approach used is based on the variational formulation applied to a cavity filled by an arbitrary number of layers and in presence of an arbitrary number of metallizations (i.e. patches and ground planes of finite dimensions). In order to numerically solve the stationary equation for the electromagnetic field, a Finite Element Method (FEM) in conjunction with a Boundary Element Method (BEM) is applied and the main scattering and radiation features of the cavity antenna are straightforwardly carried out. Some numerical results showing the effects of different complex media on the radiation pattern, on the input impedance and on the radar cross section of multi-layered cavity antennas are, finally, presented. Such results show that chiral materials allow to reduce the antenna size for a fixed working frequency increasing, besides, the cross-polarization levels. Some bianisotropic materials, instead, allow to obtain the same size reduction as chiral media without degrading the cross-polarization purity.