Terahertz (THz) technology offers novel opportunities in biology and medicine, thanks to the unique features of THz-wave interactions with tissues and cells. Among them, we particularly notice strong sensitivity of THz waves to the tissue water, as a medium for biochemical reactions and a main endogenous marker for THz spectroscopy and imaging. Tissues of the brain have an exceptionally high content of water. This factor, along with the features of the structural organization and biochemistry of neuronal and glial tissues, makes the brain an exciting subject to study in the THz range. In this paper, progress and prospects of THz technology in neurodiagnostics are overviewed, including diagnosis of neurodegenerative disease, myelin deficit, tumors of the central nervous system (with an emphasis on brain gliomas), and traumatic brain injuries. Fundamental and applied challenges in study of the THz-wave – brain tissue interactions and development of the THz biomedical tools and systems for neurodiagnostics are discussed.