Our understanding of crystal growth continues to increase thanks to progress in theoretical models, computer simulations and experimental techniques. A discussion of the state-of-the-art in morphology prediction and of the determination of the solid-liquid interface structure using X-ray diffraction shows, however, that there is still a large gap between experiment and theory. We expect that computer modelling, in the form of both Molecular Dynamics simulations and first-principle calculations, will play a crucial role in filling this gap.