The review considers disordered magnetic systems of the Griffiths type, where the magnetic disorder is caused by the dispersion of local magnetic fields. It is shown that in such systems magnetic clusters exist at temperatures both above and below the Curie point, which leads to an anomalous temperature dependence of the magnetic susceptibility in the paramagnetic phase. A striking manifestation of this type of disorder is the power-law magnetic field dependences of magnetization in the ferromagnetic phase, existing in wide ranges of temperature and magnetic field. The analysis of the parameters of the power-law functions allows constructing the order parameter for the Griffiths phase with a finite magnetic transition temperature. The developed model of magnetic properties is confirmed by experimental results for such strongly correlated systems as manganites, perovskites, cobaltites, dialuminates, pyrochlores, various intermetallics, systems with hidden order and spiral magnets. Recently synthesized substitutional solid solutions in the noncentrosymmetric MnSi-RhSi system are of special interest, as long as in this material the existence of the Griffiths phase is combined with the effect of a giant increase in the Curie temperature up to values of ~350 K (12 times with respect to MnSi), exceeding room temperature. This behavior contradicts the standard mechanism of universal suppression of the magnetic transition temperature in the Griffiths phase. To interpret this effect, the spin-polaron model can be used, which considers quasi-bound states of subnanometer size consisting of localized magnetic moments of magnetic ions and itinerant electrons. The analysis of models and experimental data shows that the study of magnetism on the nanometer scale is a promising direction for studying various disordered magnets. The review is based on the materials of the report at the session of the Physical Sciences Division of the Russian Academy of Sciences.