The applications of multiscale quantum-classical (QM-MM) approaches have shown an extraordinary expansion and diversification in the last couple of decades. A great proportion of these efforts have been devoted to interpreting and reproducing spectroscopic experiments in a variety of complex environments such as solutions, interfaces, and biological systems. Today, QM-MM-based computational spectroscopy methods constitute accomplished tools with refined predictive power. The present review summarizes the advances that have been made in QM-MM approaches to UV-visible, Raman, IR, NMR, electron paramagnetic resonance, and Mössbauer spectroscopies, providing in every case an introductory discussion of the corresponding methodological background. A representative number of applications are presented to illustrate the historical evolution and the state of the art of this field, highlighting the advantages and limitations of the available methodologies. Finally, we present our view of the perspectives and open challenges in the field.

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