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The past decade has witnessed an increasing interaction between experiment and theory in the field of molecular spectroscopy. On the computational side, ongoing developments of hardware and software have moved computational spectroscopy from a highly specialized research area to a general tool for researchers in different fields of chemical science. However, since its dawn, computational spectroscopy has been characterized by the dichotomies of qualitative and quantitative description, and of interpretation and accuracy. Indeed, the analysis of experiments is seldom straightforward because of the subtle interplay of several different effects, which are not easy to evaluate and isolate, and/or the complexity of the system under consideration. Often, the accuracy has to be set aside for a more qualitative analysis that will provide the means for a broad interpretation. In such a scenario, the most recent advances in theoretical treatments as well as computational tools have opened the way to the reconciliation of accuracy and interpretability, resulting in unequivocal analyses and assignments of experimental spectra and their unbiased interpretation. This Review aims at being a comprehensive, authoritative, critical, and readable account of general interest to the chemistry community because of the wealth of qualitative and quantitative information that can be obtained from spectroscopic investigations. Limiting ourselves to rotational and vibrational spectroscopy, emphasis will be put on accuracy and interpretability as well as on the routes toward their reconciliation and integration.