In bulk ferroelectric ceramics, extrinsic contributions associated with motion of domain walls and phase boundaries are a significant component of the measured dielectric and piezoelectric response. In thin films, the small grain sizes, substantial residual stresses, and the high concentration of point and line defects change the relative mobility of these boundaries. One of the consequences of this is that thin films typically act as hard piezoelectrics. This paper reviews the literature in this field, emphasizing the difference between the nonlinearities observed in the dielectric and piezoelectric properties of films. The effect of ac field excitation levels, dc bias fields, temperature, and applied mechanical stress are discussed.