This will be an expository talk on the mathematics of signal quantization, with an emphasis on the "one-bit" setting. The latter problem is to approximate bounded functions arbitrarily well by judiciously chosen {+1,-1} sequences. Digital halftoning (which is a crucial step in printing images) is one example of application in which this type of encoding is utilized; the analog-to-digital interface in CD players is another example. Despite the vast amount of engineering practice, the mathematical theory has remained mostly incomplete and many challenging problems still remain unsolved.