Heavy metal fluoride glasses are the backbone of modern mid-infrared fiber technology. In the last few years, optical fibers made of fluorozirconate, fluoroaluminate, and fluoroindate glasses have reached the high level of reliability that is required for their widespread use in industrial and medical applications, which explains the rapid growth of this technology. In this tutorial review, the author, who was part of the team that discovered heavy metal fluoride glasses exactly fifty years ago, provides a summary of the glass synthesis process and elucidates the most important physical properties of heavy metal fluoride glasses. Finally, a brief overview of their main application areas is presented.