Processes of forming fibers of inorganic materials in their production by means of the pendant drop melt extraction (PDME) method have been considered. An influence of the melt cooling rate (up to millions of degrees per second) on the structure and properties of fibers has been studied for metallic alloys (based on iron, nickel, cobalt, titanium, copper, aluminum, zinc and bismuth), ceramic materials, intermetallics, composite materials, and catalysts. Mechanisms of PDME-assisted formation of porous fibrous materials have been examined as well as their properties and applications. Basic principles and approaches to the development of equipment for the production of fibers have been described. Results of study on laser synthesis of oxide ceramics nanopowders have been brought.