Biological specimens such as cells, tissues and biofluids (urine, blood) contain mixtures of many different biomolecules, all of which contribute to a Raman spectrum at any given point. The separation and identification of pure biochemical components remains one of the biggest challenges in Raman spectroscopy. Multivariate curve resolution, a matrix factorization method, is a powerful, yet flexible, method that can be used with constraints, such as non-negativity, to decompose a complex spectroscopic data matrix into a small number of physically meaningful pure spectral components along with their relative abundances. This paper reviews recent applications of multivariate curve resolution by alternating least squares analysis to Raman spectroscopic and imaging data obtained either in vivo or in vitro from biological and medical samples.