Raman spectroscopy is an increasingly popular technique in many areas, including biology and medicine. It is based on Raman scattering, a phenomenon in which incident photons lose or gain energy via interactions with vibrating molecules in a sample. These energy shifts can be used to obtain information regarding molecular composition of the sample with very high accuracy. Applications of Raman spectroscopy in the life sciences have included quantification of biomolecules, hyperspectral molecular imaging of cells and tissue, medical diagnosis, and others. This review briefly presents the physical origin of Raman scattering, explaining the key classical and quantum mechanical concepts. Variations of the Raman effect will also be considered, including resonance, coherent, and enhanced Raman scattering. We discuss the molecular origins of prominent bands often found in the Raman spectra of biological samples. Finally, we examine several variations of Raman spectroscopy techniques in practice, looking at their applications, strengths, and challenges. This review is intended to be a starting resource for scientists new to Raman spectroscopy, providing theoretical background and practical examples as the foundation for further study and exploration.