Both GaN- and ZnO-based diluted semiconductors (DMSs) have recently attracted considerable interest fueled by theoretical predictions of ferromagnetic ordering in these materials above room temperature, making them especially attractive for spintronics. The intense experimental research that followed has revealed, however, a great deal of controversy. The local structure and magnetic behavior of GaN- and ZnO-based DMSs were found to depend strongly on a preparation technique and growth conditions for the materials of the same nominal composition and the reported results varied considerably from group to group. This problem highlighted clearly the lack of theoretical understanding of physical mechanisms underlying ferromagnetisms in these materials and the inadequacy of standard characterization techniques used to probe structural and magnetic properties of the DMSs. In this paper, we report on the recent progress in the theoretical and experimental studies of ZnO- and GaN-based DMSs and make special impact on critical discussion of experimental methods employed for investigation of their magnetic and optical properties.