The conclusions coming out from broad studies performed on group III-V DMSs strongly indicate presence of ferromagnetic phase in all compounds diluted with manganese, iron, or chromium. Results obtained for GaMnAs could be explained by one phase ferromagnetic material. Originally, ferromagnetic ordering of Mn spins was connected with mediation by holes from GaAs valence band (Dietl et al., 2000). Curie temperature of GaMnAs depended on Mn content as well as hole concentration. However, recently there are some suggestions that the holes in GaMnAs reside in impurity band (Alvarez and Dagotto, 2003; Berciu and Bhatt 2001; Mahadevan and Zunger, 2004a; Rokhinson et al., 2007) and it is probable that holes from Mn band, rather than from GaAs valence band, are responsible for ferromagnetism of GaMnAs. The main problem with commercialization of this ferromagnetic semiconductor is its transition to paramagnetic phase still well below 300K, and not much hope for increase of this value. In the case of GaN diluted with manganese or iron ions, ferromagnetic phase is responsible only for part of its magnetic properties. Precipitation of alien phase with its own crystalline structure within GaN, or regions rich in transition metal, resulting from spinodal decomposition to mutually coherent phases, seems to explain creation of multi- (at least two: ferromagnetic and paramagnetic) component material. However, the accounting for ferromagnetism of one of these components with well understood origin of ferromagnetism is still an open issue. The interesting system seems to be GaN diluted with chromium. For this material one phase, ferromagnetic above room temperature, was often observed. The explanation of ferromagnetic ordering cannot follow in this case the well established for DMS model of carrier mediated exchange interactions within transition metal ensemble because of lack of holes in high concentration. The proposed double-exchange mechanism (Liu et al., 2004) needs further experimental support. From the point of view of possible application - still technological effort is necessary in order to improve homogeneity of this material. Studies of group III-V DMSs showed that, for better understanding of possible magnetic ordering in DMSs, it is important to undertake research of semiconductors with transition metals of concentrations on impurity level. In this chapter it is shown clearly, mostly on the example of GaN:Mn material. The broad studies of Mn impurity in GaN: magnetic, optical and electron transport allowed to understand why the conditions of Zener's model of ferromagnetism are difficult to be fulfilled in bulk GaMnN. While studying manganese impurity in GaN, several new results connected with behavior of transition metal dopant in ionic semiconductors were obtained. One of them is a pretty high energy of lattice relaxation accompanying impurity charge transfer transitions. It was shown for the case of GaN:Mn that only when taking into account lattice relaxation, the internal reference rule for transition metal ions may be kept valid. Electron transport measurements performed on different III-V materials, doped with Mn of different concentrations, allowed determining neutral acceptor configuration of manganese in these compounds (Wolos et al., 2007). It occurred that atomic structure of such center changes in series from GaAs through InP and GaP, to GaN. In the case of GaAs, manganese stays in d5 state with hole bound to it, having localization radius of about 14 Å. This hole can be well described by wave function of GaAs valence band. Such picture is strongly supported by optical absorption with hydrogenic-like series of lines corresponding to optical transition of Mn-bound hole to its excited states (Tarhan et al., 2003), as well as by ESR signal ascribed to GaAs valence band hole bound to Mn center (Schneider et al., 1987). In the case of InP and GaP, localization radius of hole bound to Mn in d5 configuration is smaller, and it varies from 7 to 4 Å, respectively. For both InP and GaP no ESR signal due to transitions within ground state of valence band hole bound to Mn in d5 configuration was detected, what may reflect loss of valence band character of this hole in its ground state. On the other hand, hydrogenic-like series of lines in optical absorption were observed in both cases, proving hydrogenic-like character of the excited states. The extreme case is neutral acceptor configuration of manganese in GaN, for which well-localized d4 configuration was found. Absorption related to this configuration is entirely different than in the case of three other compounds, and can be explained in frame of crystal-field theory, with localized wave function restricted to the area in-between manganese ligands. With such a picture in mind one should reconsider Zener's model of ferromagnetism in semiconductors, since, not always, valence band-like holes may mediate exchange interactions in III-V DMSs. It seems justified in the case of GaMnAs material, but not necessarily in the case of Mn in InP or GaP, for which more localized holes should be considered. In the case of GaMnN the input for Zener's model is Mn in d4 or d3, and holes originating from additional shallow acceptors. Since, as it was mentioned before, it would be technologically very difficult to provide enough holes by co-doping of GaN for efficient mediation, Zener's model is not adequate for explanation of ferromagnetism observed in diluted magnetic GaN. Ferromagnetic phases detected by means of magnetization measurements need another theoretical description, although spinodal decomposition may account for existence of magnetic ion-rich phase. The problem of changes in localization of neutral Mn acceptor was acknowledged in theoretical papers of Mahadevan and Zunger (2004a, 2004b) as well as in the recent paper of Dietl (2008), who proposed a revision of the Zener's model describing ferromagnetic ordering in semiconductors (Dietl et al., 2000). It was found that when growing of GaMnN or GaFeN with high content of transition metals, secondary phases of ferromagnetic character are easily created. The exact origin of these phases, as well as mechanism of ferromagnetism of them, needs further work. Gaining knowledge about their nature, as well as gaining control over their size and density, could help with engineering of a new and interesting class of materials-semiconductor ferromagnetic composites. © 2008 Elsevier Inc. All rights reserved.