Single crystals of CdTe or dilute alloys of Cd1−yZnyTe (y ≤ 0.04) and CdTe1−zSez (z ≤ 0.04) with low defect density and large single-crystal area (>30 cm2) are required as substrates for high-quality epitaxial Hg1−xCdxTe thin films in the infrared (IR) detector industry. Bridgman or gradient freeze has been the most common current technique used for growing these materials. This paper reviews the current status and the evolution at SBRC of one variation of the Bridgman technique, viz., vertical-modified Bridgman (VMB), for producing large-area substrates with excellent uniformity and reproducibility. CdTe, Cd1−yZnyTe (y ≤ 0.04) and CdTe1−zSez (z ≤ 0.04) boules of 5-to 7.5-cm diameter have been grown unseeded in the present version of the VMB growth system. In general, under optimum growth conditions, the boules have the smallest grain structure (several grains) at the tip end with enhancement of grain selection as the cylindrical body of the boule is approached, resulting in one predominant and large grain occupying 70 to 80 percent of the entire boule volume; {111}-oriented Cd1−yZnyTe and CdTe1−zSez substrates with single-crystal areas as large as 50 to 60 cm2 have been obtained from these boules. Crystal quality characterized by x-ray rocking curve, IR transmission (2.5 to 20 µm), low-temperature photoluminescence, and Hall-effect measurements as a function of temperature, showed a strong correlation with the starting material quality (especially that of elemental Te and Se). Analyses of the thermal history during growth reveals that the presence of the ampoule (with charge) increases the temperature inside the furnace by 10 to 15 degrees. The temperature gradient at the tip was measured to be 8 to 10°C/cm and it dropped to 4 to 5°C/cm beyond 2.5 cm from the tip - where rapid enhancement of grain selection takes place in most boules. The effect of this temperature rise on the initial crystallization near the tip of a boule can be explained from the numerical thermal model that was developed for the growth process with radiative and conductive heat transfer included and using a temperature profile similar to that existing in the actual growth furnace. Conditions for maximizing the fraction solidifying with a slightly convex interface, hence maximizing the single-crystal yield are discussed.