It is sometimes said that 'our eyes can see single photons'. This article begins by finding a more precise version of that claim and reviewing evidence gathered for it up to around 1985 in two distinct realms, those of human psychophysics and single-cell physiology. Finding a single framework that accommodates both kinds of result is then a nontrivial challenge, and one that sets severe quantitative constraints on any model of dim-light visual processing. This article presents one such model and compares it to a recent experiment.