The phase transformation from liquid to solid is often tightly coupled with convective transport in the melt. Such coupled processes are significant on a broad range of scales. This book gives an overview of this field as a whole. Both theoretical and experimental studies aim to provide a fundamental understanding of the physical mechanisms involved. On the microscale, there are discussions of morphological instabilities, their finite-amplitude evolutions and the development of cells and dendrites. On the mesoscale, there are discussions of "developed" cells and dendrites and of mushy zones. On the macroscale, there are discussions of full "systems" of solidifying/melting and convecting material. Here the influence of flow on crystal-growing processes, processing by beams, spin casting, macrosegregation in casting and geological systems, and energy conversion in engineering systems are all discussed.