We consider the general problem of charged particle motion in a strong electromagnetic field of arbitrary configuration and find a universal behaviour: for sufficiently high field strengths, the radiation losses lead to a general tendency of the charge to move along the direction that locally yields zero lateral acceleration. The relativistic motion along such a direction results in no radiation losses, according to both classical and quantum descriptions of radiation reaction. We show that such a radiation-free direction (RFD) exists at each point of an arbitrary electromagnetic field, while the time-scale of approaching this direction decreases with the increase of field strength. Thus, in the case of a sufficiently strong electromagnetic field, at each point of space, the charges mainly move and form currents along local RFD, while the deviation of their motion from RFD can be calculated in order to account for their incoherent emission. This forms a general description of particle, and therefore plasma, dynamics in strong electromagnetic fields, the latter can be generated by state-of-the-art lasers or in astrophysical environments.The development of state-of-the-art high-intensity laser systems has spurred renewed interest in radiation reaction and its effect on particle dynamics in strong electromagnetic fields (see, e.g., Ref. 1 and references therein). The nature of radiation reaction has been a long-standing issue in the literature [2-4], and the developments over the last decade [5][6][7][8][9] have further clarified various aspects of this effect. Furthermore, particle and plasma dynamics in the presence of significant radiation losses appears as a difficult, but rapidly developing, field for theoretical studies [5,[10][11][12][13][14][15][16][17][18]. The interest to this field has been further increased by the discovery of several somewhat counter-intuitive phenomena, such as straggling [19,20], quenching [21], radiation reaction trapping in traveling waves [22], as well as normal [23] and anomalous [24] radiative trapping in standing waves. Despite continuous efforts on developing analytical approaches [13,15,25], the high degree of nonlinearity in many cases restricts the analysis to qualitative explanations, on the level of cause-andeffect relations, supported by numerical simulations. Therefore general theoretical approaches are needed for building up a more comprehensive picture, useful for developing experimental concepts at upcoming laser facilities [26][27][28][29], where these, and other phenomena due to radiation reaction, can be exploited for creating exotic sources of particles and radiation [30][31][32][33][34], as well as extreme states of matter [35,36].In this paper, we consider particle dynamics in a strong electromagnetic field. We show that for an arbitrary electromagnetic field, there always exists a direction that yields zero transverse acceleration and thus zero value for the dominant term of the relativistic radiation reaction force. We demonstrate that radiation reaction affec...