This is a brief review of theoretical and experimental studies of acoustic nonlinearities in porous media. Like gas bubbles in water, pores may increase the effective nonlinearity parameter of a medium by several orders at a rather small porosity. For porous solids, such phenomena can be observed in the case of ``waterlike'' media when the shear modulus is small compared to the longitudinal elastic moduli. Experiments with porous polymers have confirmed the occurrence of very strong nonlinearity and have shown a good agreement with the theory. Another problem is grainy media with fluid filling of the space between grains. Such a system is known to possess anomalously big nonlinearity due to the contact deformations (Hertz law). Here, the presence of air bubbles in the intergrain fluid is taken into account. It is shown that the presence of free gas may further increase the nonlinearity of the structure. Finally, some theoretical and experimental studies of nonlinearities in a water-saturated seabed with bubbles are outlined. Estimates made for some artificial and natural materials show a possibility to use the acoustic nonlinearity as a sensitive parameter to evaluate the medium structure.