Crystal growth conducted under microgravity conditions has had a profound impact on improving our understanding of melt crystal growth processes. Here, we present a brief history of microgravity crystal growth and discuss the development of appropriate models to interpret and optimize these growth experiments. The need for increased model realism and predictive capability demands new approaches for describing phenomena important at several disparate length scales. Of special importance is the ability to represent three-dimensional and transient continuum transport (flows, heat, and mass transfer), phase-change phenomena (thermodynamics and kinetics), and system design (such as furnace heat transfer during melt growth). An overview of mathematical models and numerical algorithms employed to represent such multiscale effects is presented.