Scaling laws associated with critical points have the power to greatly simplify our description of complex biophysical systems. We first review basic concepts and equations associated with critical phenomena for the general reader. We then apply these concepts to the specific biophysical system of lipid membranes. We recently reported that lipid membranes can contain composition fluctuations that behave in a manner consistent with the two-dimensional Ising universality class. Near the membrane's critical point, these fluctuations are micron-sized, clearly observable by fluorescence microscopy. At higher temperatures, above the critical point, we expect to find submicron fluctuations. In separate work, we have reported that plasma membranes isolated directly from cells exhibit the same Ising behavior as model membranes do. We review other models describing submicron lateral inhomogeneity in membranes, including microemulsions, nanodomains, and mean field critical fluctuations, and we describe experimental tests that may distinguish these models.