The goal of this article is to survey the matrix methods that spectroscopists and data analysts are using to recover chemical information from electronic and vibrational spectral measurements. After an introduction, we review the principles of the spectral measurements at the focus of this article as it defines notation and describes several types of spectral measurements that are either acquired or analyzed in matrix format. These include steady‐state, dynamic, and correlation data. Next, we provide a rigorous mathematical description of the most important numerical methods for matrix analysis. Finally, five classes of matrix analysis methods that have been applied to molecular spectra are surveyed: exploratory data analysis, pattern recognition, spectral calibration, curve resolution, and multiway data methods. Short discussions about software alternatives and future developments are also included. A description of the notational conventions followed and algorithm listings are also provided.