The non-equilibrium state of an undercooled melt allows the investigat
ion of various phenomena involved in the formation of metastable solid
phases. The present work reviews the present state of the art in this
field. In detail, the thermodynamics of the undercooled melt, nucleat
ion and growth processes are discussed, with special emphasis on the c
onditions of the formation of metastable states, such as metastable cr
ystalline metals, quasi-crystals, metallic glasses, supersaturated sol
utions and grain-refined materials. The techniques needed for the in-s
itu investigation of non-equilibrium solidification phenomena in under
cooled melts are discussed, and their potential for such investigation
s is evaluated. Aspects of microgravity research in this field are als
o included.