Label-free Raman microspectroscopy combined with a multivariate curve resolution (MCR) analysis can be a powerful tool for studying a wide range of biomedical molecular systems. The MCR with the alternating least squares (MCR-ALS) technique, which retrieves the pure component spectra from complicatedly overlapped spectra, has been successfully applied to in vivo and molecular-level analysis of living cells. The principles of the MCR-ALS analysis are reviewed with a model system of titanium oxide crystal polymorphs, followed by two examples of in vivo Raman imaging studies of living yeast cells, fission yeast, and budding yeast. Due to the non-negative matrix factorization algorithm used in the MCR-ALS analysis, the spectral information derived from this technique is just ready for physical and/or chemical interpretations. The corresponding concentration profiles provide the molecular component distribution images (MCDIs) that are vitally important for elucidating life at the molecular level, as stated by Schroedinger in his famous book, "What is life?" Without any a priori knowledge about spectral profiles, time- and space-resolved Raman measurements of a dividing fission yeast cell with the MCR-ALS elucidate the dynamic changes of major cellular components (lipids, proteins, and polysaccharides) during the cell cycle. The MCR-ALS technique also resolves broadly overlapped OH stretch Raman bands of water, clearly indicating the existence of organelle-specific water structures in a living budding yeast cell.