Electronic and vibrational spectroscopic studies of molecules are of crucial importance to characterizing a molecule and detecting the molecular species in different environments. In this review article, we summarized some important theoretical methods to calculate high-resolution electronic spectra and ro-vibrational states for small molecular systems with the inclusion of vibronic and ro-vibrational couplings, respectively. We have also reviewed a number of theoretical studies exploring some interesting organic chromophores like indole, isoalloxazine, transition metal trifluoride CoF3 and NiF3, and molecular ions like protonated rare gases and azido ions. These studies involve the calculation of spectroscopic features based on analytical potential energy surfaces (PESs) constructed using high-level ab initio energies. The topology of the PESs has been explored for these selected systems. The vibronic spectra and ro-vibrational states calculated using various theoretical methods and their comparison to available experimental results are reported in this review. © 2023 IOP Publishing Ltd.