The research undertaken since 20 years in our laboratory is aiming to address the problem of the relationship between the crystal growth parameters (pulling rate, thermal gradients, set-up geometry, crucible...) and the resulting crystal quality. All processes of crystal growth from the melt have been studied (Bridgman, Czochralski, Verneuil, Floating zone, shaping), applied to a variety of materials (semiconductors, oxides, halogenides). The various physical phenomena involved can be classified in: Heat transfer, which is responsible of growth rate and thermal gradients, hydrodynamics and transport, basis of intricate advection-diffusion-convection processes acting on the chemical homogeneity of the crystal, capillarity and interfaces, including crucible interactions, shape selection, nucleations... Mechanics of the solid crystal, including elasticity and plasticity, that often generate dislocations, grain boundaries, residual stresses and even cracks. A typical process engineering approach leaded to the establishment of order of magnitude relationships between the various parameters and the subsequent defects. Experiments, including growth under microgravity conditions and in a number of industrial set-ups, gave reference data. However, it was only when numerical simulation of the global process has been applied that it has been possible to understand and improve the real industrial crystal growth processes. A global approach of all the crystal growth techniques, applied to any kind of materials, has been used. Considering the interdisciplinary frame, under very large time and length scales, the emergence of a crystal growth process engineering can be postulated.