The present work discusses the existing formulae for calculation of the thermal radiation exergy. Some clarifications of terms used are given with interpretative comments. Discussed are the author's derivation procedures for three categories of radiation; enclosed system, black flux, and any arbitrary radiation flux. The formulae for radiation conversion to work or heat are established. The following peculiarities of thermal radiation are next discussed: irreversibility of emission and absorption of radiation, significance of thermal radiation exergy for a zero environment temperature, exergy of "lacking radiation", exergy at a varying environment temperature, and the analogy between exergy of substance and radiation. Utilization of solar radiation, by an absorbing surface, is evaluated and the optimum temperature of this surface is determined. The above considerations were the basis for discussing the exergy radiation formulae by Spanner and Jeter, as well as for discussing the viewpoints of Bejan and some other researchers. (C) 2003 Elsevier Ltd. All rights reserved.