There are numerous application of terahertz (THz) waves in biomedicine due to its properties that can be absorbed strongly by water in biological systems and induce resonances with the weak interaction among the biological macromolecules in the biological systems. Though there is no direct ionization damage on biological tissues due to their low photon energies, THz waves would bring a series of biological effects on the biological cells and tissues with increase of the intensity of the THz beam. Different irradiation conditions such as the parameters of the THz waves and the different biological systems will result in different biological effects, including mainly the thermal effects and non-thermal effects. In this paper, we discuss firstly the physical mechanisms of these two kinds of effects, then introduce the current main THz sources suitable for research of the biological effects, and summarize the typical biological effects in detail and the research progress in this field. Finally we prospect the potential applications and challenges of the research on biological effects.