Applications of EPR and ENDOR simulations of relevance in radiation research involving free radicals, radical pairs, triplet states and to less extent metal complexes are treated. Early fundamental work involving in situ radiolysis of liquids and stickplot analysis of spectra is reviewed, while single crystal analysis is only briefly discussed. The analysis of data obtained with continuous wave methods of species trapped in disordered solids, "powders" is emphasized. Simulations based on first and second order and exact theory are described and exemplified. Methods to obtain parameters for the dynamics of radicals in irradiated solids and for the simulation of spectra at microwave saturation are discussed. Procedures for the simulation of powder ENDOR spectra of radicals are described in detail, with special emphasis on the influence of nuclear quadrupole couplings due to nuclei with I ≥ 1. EPR and ENDOR simulation programs known to us are presented in an Appendix, including addresses for downloading when available.