Mesoscopic phenomena in nanostructures that incorporate diluted magnetic semiconductors may exhibit a number of novel features driven by spin interactions between mobile electrons and localized spins. Millikelvin studies of linear and nonlinear diffusive charge transport, which have been carried out for submicron wires of epilayers as well as for microstructures of bicrystals, are reviewed. These studies have provided information on the significance of spin-disorder scattering and evidence of a new driving mechanism of the magnetoconductance fluctuations - the redistribution of the electrons between energy levels of the system, induced by the giant s - d exchange spin-splitting. Important implications of these findings for previous interpretations of spin effects in semiconductor and metal nanostructures are discussed.