The U.S. commercial nuclear-power industry consists of 104 operating nuclear units on 66 sites, that produce about 20% of U.S. electricity. From the beginning, the concern with safety (that is, with the possibility of a major accident that would release radioactivity in large amounts) has been the paramount issue for the designers and operators of these plants as well as for the public. Many different means are available for estimating how much "safety" is achieved, and they provide different insights. However, by any of these measures, the safety of the operating plants has been improving dramatically over the last couple of decades. This talk will explain how nuclear engineers understand what safety levels are being achieved, will describe the evidence for the significant improvements that have occurred, and will discuss why the improvements have occurred.