Undercooling of liquids is a common occurrence in solidification. The
level of undercooling influences both the microstructural development
by controlling phase selection during nucleation and the morphological
evolution during the growth phase of solidification. The development
of large liquid undercooling is linked to kinetic control of solidific
ation processes including suppression of heterogeneous nucleation duri
ng slow cooling and constrained growth during rapid quenching. The dee
pest undercoolings have been measured in droplet samples and approach
0.3-0.4 . T-m. At high undercooling, solidification can yield metastab
le product structures, whose constituents are the result of kinetic co
mpetition which usually is determined during the nucleation phase and
controlled by heterogeneous nucleation. Recently, theoretical, experim
ental and simulation advances have led to a better understanding of nu
cleation catalysis reactions and the influence of thermal history duri
ng processing at high and low undercoolings. Detailed analysis of the
kinetic competition process during solidification along with novel exp
eriments have probed the limits of nucleation theory in both size and
time scales and have stimulated new developments in theoretical modeli
ng and computer simulation studies.