Liquid helium in the superfluid phase behaves as if a fraction of the liquid has zero viscosity—the liquid flows through narrow tubes even when there is no pressure gradient across the tubes' ends. This “superfluid fraction” is zero above the critical temperature for the onset of superfluidity, and it increases to unity when the temperature is decreased to absolute zero in the superfluid phase. When pure helium is three dimensional—for example, when it fills a beaker—the critical temperature for superfluidity is 2.17 K. When only a thin film of helium covers a plane substrate, however, the critical temperature depends on the film thickness and the substrate. Since the late 1970s, when our understanding of the superfluid transition in two and three dimensions was essentially completed, experimenters have been studying the superfluid transition when helium fills pores, on the order of a few tens of angstroms in size, in highly connected porous structures. These experiments have shown features in the past few years that both theorists and experimenters say they do not understand.