High-pressure and time-resolved studies of the optical emission from n-type doped GaN/AlN multi-quantum-wells (MQWs) with various well thicknesses are analysed in comparison with ab initio calculations of the electronic (band structure, density of states) and optical (emission energies and their pressure derivatives, oscillator strength) properties. The optical properties of GaN/AlN MQWs are strongly affected by quantum confinement and polarization-induced electric fields. Thus, the photoluminescence (PL) peak energy decreases by over 1 eV with quantum well (QW) thicknesses increasing from 1 to 6 nm. Furthermore, the respective PL decay times increased from about 1 ns up to 10 μs, due to the strong built-in electric field. It was also shown that the band gap pressure coefficients are significantly reduced in MQWs as compared to bulk AlN and GaN crystals. Such coefficients are strongly dependent on the geometric factors such as the thickness of the wells and barriers. The transition energies, their oscillator strength, and pressure dependence are modeled for tetragonally strained structures of the same geometry using a full tensorial representation of the strain in the MQWs under external pressure. These MQWs were simulated directly using density functional theory calculations, taking into account two different systems: the semi-insulating QWs and the n-doped QWs with the same charge density as in the experimental samples. Such an approach allowed an assessment of the impact of n-type doping on optical properties of GaN/AlN MQWs. We find a good agreement between these two approaches and between theory and experimental results. We can therefore confirm that the nonlinear effects induced by the tetragonal strain related to the lattice mismatch between the substrates and the polar MQWs are responsible for the drastic decrease of the pressure coefficients observed experimentally.