Abstract
A homogeneous-nucleation-based (HNB) crystallization, which has been discovered at the low temperatures of glass transition temperature region in fragile liquids showing non-Arrhenius properties in the temperature dependence of structural relaxation times, is explained with summarizing classical theories for homogeneous nucleation and crystal growth. The mechanism of HNB crystallization is elucidated, which makes a microscopic homogeneous crystal nucleation process observable macroscopically as the crystallization, and the structural relaxation process of liquids which governs the homogeneous nucleation rates is discussed based on the magnitude and the temperature dependence of HNB crystallization rates.