Machine learning has become more and more popular in computational chemistry, as well as in the important field of spectroscopy. In this concise review, we walk the reader through a short summary of machine learning algorithms and a comprehensive discussion on the connection between machine learning methods and vibrational spectroscopy, particularly for the case of infrared and Raman spectroscopy. We also briefly discuss state-of-the-art molecular representations which serve as meaningful inputs for machine learning to predict vibrational spectra. In addition, this review provides an overview of the transferability and best practices of machine learning in the prediction of vibrational spectra as well as possible future research directions.