A tutorial article is presented for the use of linear and nonlinear Raman microspectroscopies in biomedical diagnostics. Coherent anti-Stokes Raman scattering (CARS) is the most frequently applied nonlinear variant of Raman spectroscopy. The basic concepts of Raman and CARS are introduced first, and subsequent biomedical applications of Raman and CARS are described. Raman microspectroscopy is applied to both in-vivo and in-vitro tissue diagnostics, and the characterization and identification of individual mammalian cells. These applications benefit from the fact that Raman spectra provide specific information on the chemical composition and molecular structure in a label-free and nondestructive manner. Combining the chemical specificity of Raman spectroscopy with the spatial resolution of an optical microscope allows recording hyperspectral images with molecular contrast. We also elaborate on interfacing Raman spectroscopic tools with other technologies such as optical tweezing, microfluidics and fiber optic probes. Thereby, we aim at presenting a guide into one exciting branch of modern biophotonics research.