This paper reviews the present understanding of the origin of ferromagnetic response thathas been detected in a number of diluted magnetic semiconductors (DMSs) and dilutedmagnetic oxides (DMOs) as well as in some nominally magnetically undoped materials. Itis argued that these systems can be grouped into four classes. To the first belongcomposite materials in which precipitations of a known ferromagnetic, ferrimagnetic orantiferromagnetic compound account for magnetic characteristics at high temperatures.The second class forms alloys showing chemical nanoscale phase separation into the regionswith small and large concentrations of the magnetic constituent. Here, high-temperaturemagnetic properties are determined by the regions with high magnetic ion concentrations,whose crystal structure is imposed by the host. Novel methods enabling a controlof this spinodal decomposition and possible functionalities of these systems aredescribed. To the third class belong (Ga, Mn)As, heavily doped p-(Zn, Mn)Te,and related semiconductors. In these solid solutions the theory built on the p–dZener model of hole-mediated ferromagnetism and on either the Kohn–Luttingerkp theory or the multi-orbital tight-binding approach describes qualitatively, and oftenquantitatively, thermodynamic, micromagnetic, optical, and transport properties.Moreover, the understanding of these materials has provided a basis for the development ofnovel methods, enabling magnetization manipulation and switching. Finally, in anumber of carrier-doped DMSs and DMOs a competition between long-rangeferromagnetic and short-range antiferromagnetic interactions and/or the proximity of thelocalization boundary lead to an electronic nanoscale phase separation. Thesematerials exhibit characteristics similar to colossal magnetoresistance oxides.