In this review, we describe dielectric properties of biological tissues and liquids in the context of terahertz (THz) biophotonics. We discuss a model of the THz dielectric permittivity of water and water-containing media, which yields analysis of the relaxation and damped resonant molecules modes. We briefly describe modern techniques of THz spectroscopy and imaging employed in biophotonics with a strong emphasize on a THz time-domain spectroscopy. Furthermore, we consider the methods of sub-wavelength resolution THz imaging and the problem of THz wave delivery to hard to access tissues and internal organs. We consider the THz dielectric properties of biological solutions and liquids. Although strong absorption by water molecules prevents THz-waves from penetration of hydrated tissues and probing biological molecules in aqueous solutions, we discuss approaches for overcoming these drawbacks – novel techniques of freezing and temporal dehydration by application of hyperosmotic agents which have a potential for cancer detection. We review recent applications of THz technology in diagnosis of malignancies and aiding histology paying particular attention to the origin of contrast observed between healthy and pathological tissues. We consider recent applications of THz reflectometry in sensing the thinning dynamics of human pre-corneal tear film. Modern modalities of THz imaging, which relies on the concepts of multi-spectral and multi-temporal domains and employing the principles of color vision, phase analysis and tomography are discussed. Novel methods of THz spectra analysis based on machine learning, pattern recognition, chemical imaging and the revealing of the spatial distribution of various substances in a tissue, are analyzed. Advanced thermal model describing biological object irradiated by THz waves and phantoms mimicking the optical properties of tissues at THz frequencies are presented. Finally, application of the high-resolution THz spectroscopy in analytic chemistry, biology and medicine are described.