Molecular spectroscopy measures transitions between discrete molecular energies which follow quantum mechanics. Structural information of a molecule is encoded in the spectra, which can be only decoded using quantum mechanics and therefore computational molecular spectroscopy becomes essential. In this review perspective, the role evolution of computational molecular spectroscopy has been discussed with several joint theory and experiment spectroscopic studies in the past decades, which includes rotational (microwave), vibrational and electronic spectroscopy (valence and core) of molecules. With the development in high resolution and computerized synchrotron sourced spectroscopy, spectral measurements and computational molecular spectroscopy need to be integrated for materials development. Contemporary computational molecular spectroscopy is, therefore, more than merely supporting interpretation but leading the innovation. Future development of molecular spectroscopy lies to identify the niche to integrate experimental and computational molecular spectroscopy. It also requires to engineer molecular spectroscopic databases that function according to the universal approaches of computing, such as those in a Turing machine, to be realized in a chemical and/or spectroscopic programable manner (digital twinning research) in the future.