Granular ferromagnet-insulator solids consist of nanometer size ferromagnetic granules embedded in an insulating medium. They display a wide variety of magnetic, transport, optical and magneto-optical properties related to their unique nanostructure. For example, close to the percolation threshold they exhibit tunneling magnetoresistance, giant extraordinary Hall effect, nonlinear transport and optical phenomena and so on. The specific mechanisms of these effects are far from being well understood, the simple models based on the percolation theory, mean-field approaches or developed by analogy with spin-dependent transport in multilayers are not appropriate. On the other hand a significant interest to magnetic nanocomposites has been triggered by possible applications of the above effects to the development of magnetic sensors, magnetic heads, discontinuous metal-insulator spin-valve elements, high frequency magneto-impedance and magneto-optical devices etc. In addition, due to the extremely high precision of magnetic measurements magnetic nanocomposites are very suitable for study of percolation models, relevant for many problems in physics, mathematics, and life science. In the discussion, I will present some recent theoretical and experimental results on magnetotransport and magneto-optical properties of magnetic nanocomposites, focusing on compositions close to the percolation threshold. In particular, I will discuss the possible mechanisms of giant extraordinary Hall effect, field-dependent tunneling thermoelectric power, magneto-optical spectra in a wide spectrum range, enhanced magneto-optical response, non-linearity of magneto-optical phenomena with respect to magnetization and intensity of light, and magnetorefractive effect.