The availability of large, single crystals of cadmium zinc telluride (CZT) with uniform properties would lead to improved performance of gamma radiation detectors fabricated from them. However, even though CZT crystals are the central element of these systems, there remains relatively little fundamental understanding about how these crystals grow and, especially, how crystal growth conditions affect the properties of grown crystals. This paper discusses the many challenges of growing better CZT crystals and how modeling may favorably impact these challenges. Our thesis is that crystal growth modeling is a powerful tool to complement experiments and characterization. It provides an important approach to close the loop between materials discovery, device research, systems performance, and producibility. Specifically, we discuss our efforts to model gradient freeze furnaces used to grow large CZT crystals at Pacific Northwest National Laboratories and Washington State University. Model results are compared with experimental measurements, and the insight gained from modeling is discussed.