It appears paradoxical that science is producing outstanding new results and theories at a rapid rate at the same time that researchers are identifying serious problems in the practice of science that cause many reports to be irreproducible and invalid. Certainly, the practice of science needs to be improved, and scientists are now pursuing this goal. However, in this perspective, we argue that this seeming paradox is not new, has always been part of the way science works, and likely will remain so. We first introduce the paradox. We then review a wide range of challenges that appear to make scientific success difficult. Next, we describe the factors that make science work—in the past, present, and presumably also in the future. We then suggest that remedies for the present practice of science need to be applied selectively so as not to slow progress and illustrate with a few examples. We conclude with arguments that communication of science needs to emphasize not just problems but the enormous successes and benefits that science has brought and is now bringing to all elements of modern society.