The biophysical underpinning of the lipid-raft concept in cellular membranes is the liquid-ordered phase that is induced by moderately high concentrations of cholesterol. Although the crucial feature is the coexistence of phase-separated fluid domains, direct evidence for this in mixtures of cholesterol with a single lipid is extremely sparse. More extensive evidence comes from ternary mixtures of a high chain-melting lipid and a low chain-melting lipid with cholesterol, including those containing sphingomyelin that are taken to be a raft paradigm. There is, however, not complete agreement between the various phase diagrams and their interpretation. In this review, the different ternary phase diagrams of cholesterol-containing systems are presented in a uniform way, using simple x,y-coordinates to increase accessibility for the non-specialist. It is then possible to appreciate the common features and examine critically the discrepancies and hence what direct biophysical evidence there is that supports the raft concept.