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The last two decades have witnessed an increasing interest in the use of the so-called rapid analytical methods or high throughput techniques. Most of these applications reported the use of vibrational spectroscopy methods (near infrared (NIR), mid infrared (MIR), and Raman) in a wide range of samples (e.g., food ingredients and natural products). In these applications, the analytical method is integrated with a wide range of multivariate data analysis (MVA) techniques (e.g., pattern recognition, modelling techniques, calibration, etc.) to develop the target application. The availability of modern and inexpensive instrumentation together with the access to easy to use software is determining a steady growth in the number of uses of these technologies. This paper underlines and briefly discusses the three critical pillars—the sample (e.g., sampling, variability, etc.), the spectra and the mathematics (e.g., algorithms, pre-processing, data interpretation, etc.)—that support the development and implementation of vibrational spectroscopy applications.