Vibrational spectroscopy, both infrared absorption and Raman spectroscopy, have attracted increasing attention for biomedical applications, from in vivo and ex vivo disease diagnostics and screening, to in vitro screening of therapeutics. There remain, however, many challenges related to the accuracy of analysis of physically and chemically inhomogeneous samples, across heterogeneous sample sets. Data preprocessing is required to deal with variations in instrumental responses and intrinsic spectral backgrounds and distortions in order to extract reliable spectral data. Data postprocessing is required to extract the most reliable information from the sample sets, based on often very subtle changes in spectra associated with the targeted pathology or biochemical process. This review presents the current understanding of the factors influencing the quality of spectra recorded and the pre-processing steps commonly employed to improve on spectral quality. It further explores some of the most common techniques which have emerged for classification and analysis of the spectral data for biomedical applications. The importance of sample presentation and measurement conditions to yield the highest quality spectra in the first place is emphasised, as is the potential of model simulated datasets to validate both pre- and post-processing protocols.