Rapid solidification processing is widely used in industry, but the underlying mechanisms are not completely understood. In the present work, an effort is made to understand the effects of rapid heat extraction and large undercooling on the solidification sequence, in particular: (1) the transition from diffusion-limited growth to impingement-limited growth; and (2) crystal nucleation in deeply undercooled liquids. Rapid solidification can be achieved either by (1) rapid quenching, or (2) large undercooling. Accordingly, two different methods are used in the present work. They are, (a) nanosecond pulsed laser quenching, and (b) bulk undercooling in a liquid flux. Thin films prepared by d.c. magnetron getter sputtering have been used in pulsed laser quenching. Both pure metals (Fe, Zr, Ti, Co, Ge) and binary alloys (Nb-Ni, Ti-Co) prepared by this method are investigated. Alloys Fe<SUB>40</SUB>Ni<SUB>40</SUB>B<SUB>20</SUB>, Ni<SUB>75</SUB>Si<SUB>8</SUB>B<SUB>17</SUB> and elemental Ge have been used in bulk undercooling. The metastable structures obtained are analysed by optical microscopy, scanning electron microscopy, electron probe microanalysis, transmission electron microscopy and X-ray diffraction. The results obtained are discussed in terms of non-equilibrium crystal nucleation and growth processes.