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Flash memory grew from a simple concept in the early 1980s to a technology that generated close to $23 billion in worldwide revenue in 2007, and this represents one of the many success stories in the semiconductor industry. This success was made possible by the continuous innovation of the industry along many different fronts. In this paper, the history, the basic science, and the successes of fash memories are briefly presented. Flash memories have followed the Moore's Law scaling trend for which finer line widths, achieved by improved lithographic resolution, enable more memory bits to be produced for the same silicon area, reducing cost per bit. When looking toward the future, significant challenges exist to the continued scaling of flash memories. In this paper, I discuss possible areas that need development in order to overcome some of the size-scaling challenges. Innovations are expected to continue in the industry, and flash memories will continue to follow the historical trend in cost reduction of semiconductor memories through the rest of this decade.