We give a brief overview on the more than 50 years of development of the moment-based image description, the moment invariants, and the orthogonal moments. Some basic ideas for significantly improving the performance of the image moment-based methods, such as the use of the low-order radial moments for reducing information suppression drawback and the separation of the radial basis from the circular harmonic basis for a free selection of the orthogonal radial polynomials, are presented. Performance measures for the orthogonal moments are discussed from the point of view of image analysis. A moment family list is proposed, which includes most of the representative moments in use and the discrete orthogonal moments.