This is a review of relevant Raman spectroscopy (RS) techniques and their use in structural biology, biophysics, cells, and tissues imaging towards development of various medical diagnostic tools, drug design, and other medical applications. Classical and contemporary structural studies of different water-soluble and membrane proteins, DNA, RNA, and their interactions and behavior in different systems were analyzed in terms of applicability of RS techniques and their complementarity to other corresponding methods. We show that RS is a powerful method that links the fundamental structural biology and its medical applications in cancer, cardiovascular, neurodegenerative, atherosclerotic, and other diseases. In particular, the key roles of RS in modern technologies of structure-based drug design are the detection and imaging of membrane protein microcrystals with the help of coherent anti-Stokes Raman scattering (CARS), which would help to further the development of protein structural crystallography and would result in a number of novel high-resolution structures of membrane proteins—drug targets; and, structural studies of photoactive membrane proteins (rhodopsins, photoreceptors, etc.) for the development of new optogenetic tools. Physical background and biomedical applications of spontaneous, stimulated, resonant, and surface- and tip-enhanced RS are also discussed. All of these techniques have been extensively developed during recent several decades. A number of interesting applications of CARS, resonant, and surface-enhanced Raman spectroscopy methods are also discussed.