Absorption and magnetic circular dichroism (MCD) spectroscopies are powerful and simple methods to discriminate among various compounds. Polycyclic aromatic hydrocarbons provide particularly strong signal, which, for example, facilitates their detection in the environment. However, interpretation of the spectra is often based on quantum-chemical simulations, providing a limited precision only. In the present work, we use time-dependent density functional theory and complete active space second-order perturbation theories to understand spectral features observed in a series of naphthalene, anthracene, phenanthrene, and three larger compounds. The electronic computations provided reasonable agreement with the experiment for the smaller molecules, while a large error persisted for the bigger ones. However, many discrepancies could be explained by vibrational splitting of the electronic transitions across the entire spectral range. Compared to plain absorption, MCD spectral bands and their vibrational splitting were more specific for each aromatic molecule. The computational tools allowing simulations of detailed vibrational features in the electronic spectra thus promise to open a qualitatively new chapter in the spectroscopy of aromatic compounds.