A distinctive feature of this review is a critical analysis of methods and results of measurements of the optical properties of tissues in a wide spectral range from deep UV to terahertz waves. Much attention is paid to measurements of the refractive index of biological tissues and liquids, the knowledge of which is necessary for the effective application of many methods of optical imaging and diagnostics. The optical parameters of healthy and pathological tissues are presented, and the reasons for their differences are discussed, which is important for the discrimination of pathologies and the demarcation of their boundaries. When considering the interaction of terahertz radiation with tissues, the concept of an effective medium is discussed, and relaxation models of the effective optical properties of tissues are presented. Attention is drawn to the manifestation of the scattering properties of tissues in the THz range and the problems of measuring the optical properties of tissues in this range are discussed. In conclusion, a method for the dynamic analysis of the optical properties of tissues under optical clearing using an application of immersion agents is presented. The main mechanisms and technologies of optical clearing, as well as examples of the successful application for differentiation of healthy and pathological tissues, are analyzed.