Is the Universe of infinite extent, or is it a finite system? Will it expand forever, or will it reach some maximum size before turning and collapsing upon itself like an inverse Big Bang? Just a few years ago, models of the conventional Friedman types were showing consistent, albeit tentative, evidence for an open, ever-expanding Universe. Since then, further data and theory have inevitably conspired to blur the appealing simplicity of that picture. In this article I will show how the Friedman models fare in the light of new developments—particularly the recognition of a whole new class of evolutionary corrections to the properties of distant galaxies (see figure 1), and a proposed reinstatement of Einstein's disinherited cosmological constant. We shall see that the basic questions, posed above, are still unanswered.