An increasing interest in the area of biological effects at exposure of tissues and cells to the terahertz (THz) radiation is driven by a rapid progress in THz biophotonics, observed during the past decades. Despite the attractiveness of THz technology for medical diagnosis and therapy, there is still quite limited knowledge about safe limits of THz exposure. Different modes of THz exposure of tissues and cells, including continuous-wave versus pulsed radiation, various powers, and number and duration of exposure cycles, ought to be systematically studied.We provide an overview of recent research results in the area of biological effects at exposure of tissues and cells to THz waves.We start with a brief overview of general features of the THz-wave-tissue interactions, as well as modern THz emitters, with an emphasis on those that are reliable for studying the biological effects of THz waves. Then, we consider three levels of biological system organization, at which the exposure effects are considered: (i) solutions of biological molecules; (ii) cultures of cells, individual cells, and cell structures; and (iii) entire organs or organisms; special attention is devoted to the cellular level. We distinguish thermal and nonthermal mechanisms of THz-wave-cell interactions and discuss a problem of adequate estimation of the THz biological effects' specificity. The problem of experimental data reproducibility, caused by rareness of the THz experimental setups and an absence of unitary protocols, is also considered.The summarized data demonstrate the current stage of the research activity and knowledge about the THz exposure on living objects.This review helps the biomedical optics community to summarize up-to-date knowledge in the area of cell exposure to THz radiation, and paves the ways for the development of THz safety standards and THz therapeutic applications.