In this paper, we present an efficient method to classify complex electromagnetic materials. This method is based on the directional interaction of incident circularly polarized waves with the materials being tested. The presented method relies on an algorithm that classifies the test materials to one of the following categories: isotropic, chiral, bi-isotropic, symmetric anisotropic or general bianisotropic. The transmitted and reflected fields of right-handed and left-handed circularly polarized waves normally incident from three orthogonal orientations are utilized to determine the reflection/transmission coefficients and complex refractive indices. Both analytical and numerical solutions are used to compute fields of the circularly polarized waves from the arbitrary complex material slab. The complex materials are discriminated accordingly and then classified under an appropriate category. Additionally, new results for material characterization by extracting the scalar/tensorial parameters of bi-isotropic and gyrotropic materials are presented.