We review the advances of terahertz (THz) science and technology in biophotonics, including related challenges and solutions. The main impediment to THz spectroscopy and imaging in this field is the high absorption of the THz beam in water. Hence, transmission imaging and spectroscopy of thick wet tissue using THz radiation has generally been quite difficult. However, the absorption of THz waves by water molecules is so strong that increasing the power of the THz source can lead to structural and functional changes in tissues, so solutions must go beyond a larger power output. In terms of resolution, THz imaging is superior to ultrasound but inferior to visible light microscopy. Owing to its unique material analysis capabilities, promising diagnosis applications have been demonstrated through THz imaging and spectroscopy. Unfortunately, many applications are limited by beam penetration depth and resolution. Hence, researchers from a wide variety of scientific and technical fields have been actively improving these features through the development of electronic devices and materials. In addition, groundbreaking optical architecture and materials to reduce beam absorption in the optics of a system and generate focused beams with smaller diameters have been proposed. On the software side, image processing techniques to computationally enhance the resolution and quality of THz imaging have been proposed. Data science and machine learning to automate the diagnosis of defects and diseases through processing THz images and spectroscopy data have been proposed. We have reviewed the applications of THz radiation in biophotonics and research achievements toward advancing these applications. A conclusion with a roadmap toward increasing the footprint of the THz technology in biophotonics is also proposed.