In this paper we review studies aiming at elucidation of the mechanisms responsible for anomalously low pressure coefficients of the light emission energy, dEE/dP, observed in quantum structures of InGaN/GaN and GaN/AlGaN. We have established that in hexagonal InGaN/GaN and GaN/AlGaN structures the main mechanism involved is related to the pressure induced increase of the piezoelectric field which determines also the strong red shift of the emission energy with thickness of the quantum well. To reproduce the experimental findings in InGaN/GaN case, it is necessary to take into account the dependence of the piezoelectric constants on the volume-conserving strain. Whereas the experimental results on a decrease of dEE/dP in GaN/AlGaNstructures can be fully accounted for within the linear elasticity theory. In contrast to these findings, dEE/dP magnitude measured in cubic InGaN/GaN quantum structures shows value close to changes of the InGaN bangap with pressure obtained from first principle calculations. The latter result is consistent with the absence of the built-in electric fields in the cubic nitride structures.