The study of effects of ionizing radiation (IR) on plants is important in relation to several problems: (I) the existence of zones where background radiation - either natural or technogenic - is increased; (II) the problems of space biology; (III) the use of IR in agricultural selection; (IV) general biological problems related to the fundamental patterns and specifics of the effects of IR on various living organisms. By now, researchers have accumulated and systematized a large body of data on the effects of IR on the growth and reproduction of plants, as well as on the changes induced by IR at the genetic level. At the same time, there is a large gap in understanding the mechanisms of IR influence on the biochemical and physiological processes - despite the fact that these processes form the basis determining the manifestation of IR effects at the level of the whole organism. On the one hand, the activity of physiological processes determines the growth of plants; on the other, it is determined by changes at the genetic level. Thus, it is the study of IR effects at the physiological and biochemical levels that can give the most detailed and complex picture of IR action in plants. The review focuses on the effects of radiation on the essential physiological processes, including photosynthesis, respiration, long-distance transport, the functioning of the hormonal system, and various biosynthetic processes. On the basis of a large body of experimental data, we analyze dose and time dependences of the IR-induced effects - which are qualitatively similar - on various physiological and biochemical processes. We also consider the sequence of stages in the development of those effects and discuss their mechanisms, as well as the cause-effect relationships between them. The primary IR-induced physicochemical reactions include the formation of various forms of reactive oxygen species (ROS) and are the cause of the observed changes in the functional activity of plants. The review emphasizes the role of hydrogen peroxide, a long-lived ROS, not only as a damaging agent, but also as a mediator - a universal intracellular messenger, which provides for the mechanism of long-distance signaling. A supposition is made that IR affects physiological processes mainly by violating the regulation of their activity. The violation seems to become possible due to the fact that there exists a crosstalk between different signaling systems of plants, such as ROS, calcium, hormonal and electrical systems. As a result of both acute and chronic irradiation, an increase in the level of ROS can influence the activity of a wide range of physiological processes - by regulating them both at the genetic and physiological levels. To understand the ways, by which IR affects plant growth and development, one needs detailed knowledge about the mechanisms of the processes that occur at the (i) genetic and (ii) physiological levels, as well as their interplay and (iii) knowledge about regulation of these processes at different levels.