The review presents a new procedure for determination of the mechanical, electromagnetic, geometric and deformational properties of diatomic molecules from their high-resolution infrared (IR)) and microwave (MW) spectra. The mechanical properties of the molecule include the Born-Oppenheimer (BO) internuclear potential, adiabatic and nonadiabatic corrections, while the electromagnetic properties are represented by the dipole moment, electric polarisation and rotational g-factor related to the magnetic moment of the molecule. The geometry of the molecule is characterized by the BO equilibrium distance between the nuclei in the ground and in the excited rotation-vibrational (RV) states, and the deformational properties are given by the molecule susceptibility to the rotation-induced centrifugal deformation. The new procedure is presented in the numerically-analytical and pure analytical versions based on free and constrained parameters and the potential energy function expanded in the power series of a new generation or combination of power series and Padé approximants or in the form of fraction continued expansion. In the final part of the review the problem of a  “tuning-up” of the statistical indicators of the goodness of fit with physical significance of the outputs produced by fitting procedures is discussed.  The results of the numerical test of the proposed method univocally show that it is a reliable and effective tool for quantitative analysis of high-resolution IR and MW spectra of neutral and ionic diatomic systems.