Increasing computer power and the development of user-friendly, yet highly sophisticated bandstructure programs have made it possible that theoretical EFG calculations can nowadays be performed for fairly complex materials science problems. We show that a combination of these theoretical calculations with experimentally obtained quadrupole splittings can lead to new insight into various interesting problems. This is illustrated for the determination of nuclear quadrupole moments, investigations of samples containing impurities or other imperfections and for Na2[Fe(CN)5NO], a promising material for holographic storage applications.