The piezoelectric effect in polar semiconductor has seen increased interest in recent years because of the prospect of exploiting semiconducting behavior and piezoelectric response, i.e. generating electric fields in response to pressure, in novel optoelectronic devices with applications as pressure sensors and energy harvesting. In this paper we review the basic concepts and recent findings related to the novel concept of non-linear piezoelectricity, which can be exploited in composite nanostructured materials to increase the piezoelectric response compared to bulk materials. Applications to light emitting diodes and nanowires will also be discussed. We will show how the non-linear theory of piezoelectricity can in some cases lead to opposite predictions compared to the classic linear theory.