In this review, we provide a perspective on the science and technology of vitrification of waste. First, we provide a background on the general classes of wastes for which vitrification is currently used for immobilization or is proposed, including nuclear and industrial hazardous wastes. Next, we summarize the issues surrounding solubility of waste ions and resulting uncontrolled crystallization or phase separation. Some newer waste form designs propose a controlled crystallization, resulting in a glass-ceramic. A summary of glass systems and glass-ceramic systems is given, with the focus on immobilizing waste components at high waste loading. Throughout, design and processing considerations are given, and the difference between uncontrolled undesirable and controlled desirable crystallization is offered.