Vitrification from the molten state hinges on averting crystallization during the cooling path. On the other hand, critical natural processes, such as the formation of snow and igneous rocks, like obsidian, and technological operations, for example, solidification of metallic alloys and glass ceramization, illustrate the utmost importance of crystallization in our environment and technology. The structural rearrangements fostered by crystal nucleation and growth cause drastic changes in the macroscopic properties of glass-forming melts and magmas. In this article, we summarize and discuss the applicability of the most accepted models to describe crystal nucleation, growth, and overall crystallization in glass-forming systems....

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