In this paper, a historical review of the developments in the safety of LWR power plants is presented. The paper reviews the developments prior to the TMI-2 accident, i.e. the concept of the defense in depth, the design basis, the large LOCA technical controversies and the LWR safety research programs. The TMI-2 accident, which became a turning point in the history of the development of nuclear power is described briefly. The Chernobyl accident, which terrified the world and almost completely curtailed the development of nuclear power is also described briefly. The great international effort of research in the LWR design-base and severe accidents, which was, respectively, conducted prior to and following the TMI-2 and Chernobyl accidents is described next. We conclude that with the knowledge gained and the improvements in plant organisation/management and in the training of the staff at the presently-installed nuclear power stations, the LWR plants have achieved very high standards of safety and performance. The Generation 3+LWR power plants, next to be installed, may claim to have reached the goal of assuring the safety of the public to a very large extent. This review is based on the historical developments in LWR safety that occurred primarily in USA, however, they are valid for the rest of the Western World. This review can not do justice to the many fine contributions that have been made over the last fifty years to the cause of LWR safety. We apologize if we have not mentioned them. We also apologize for not providing references to many of the fine investigations, which have contributed towards LWR safety earning the conclusions that we describe just above.