Modeling is an indispensable tool for understanding and improving the growth of bulk, single crystals. Such crystals are required for the fabrication of the electronic and photonic devices that enable information technology, communications, sensing, solid-state lighting, solar energy production, and many other applications. These materials are much more than simply very pure, specialty chemicals. They must meet strict requirements for solid-state structural perfection and must be produced with high yields and low costs. Successful manufacturing techniques have been developed that utilize thermodynamic phase change to solidify a high-temperature melt into a crystal of high quality. However, harsh conditions and batch operation limit both diagnostic measurements and data available to connect growth conditions to outcomes, making modeling even more important for process improvement. Challenges and opportunities are discussed for melt crystal growth processes, with research examples that demonstrate how modeling has provided important insight into crystal-melt interface shape, dopant segregation, morphological instability, and defect formation.