We are in the midst of a shift towards using novel polynomials to decompose wavefront aberrations in a more ophthalmologically relevant way. Zernike polynomials have useful mathematical properties but fail to provide clinically relevant wavefront interpretation and predictions. We compared the distribution of the eye's aberrations and demonstrate some clinical applications of this using case studies comparing the results produced by the Zernike decomposition and evaluating them against the lower degree/higher degree (LD/HD) polynomial decomposition basis which clearly dissociates the higher and lower aberrations. In addition, innovative applications validate the LD/HD polynomial basis. Absence of artificial reduction of some higher order aberrations coefficients lead to a more realistic analysis. Here we summarize how wavefront analysis has evolved and demonstrate some of its new clinical applications.