Lateral organization in the plane of the plasma membrane is an important driver of biological processes. The past dozen years have seen increasing experimental support for the notion that lipid organization plays an important role in modulating this heterogeneity. Various biophysical mechanisms rooted in the concept of liquid-liquid phase separation have been proposed to explain diverse experimental observations of heterogeneity in model and cell membranes with distinct but overlapping applicability. In this review, we focus on the evidence for and the consequences of the hypothesis that the plasma membrane is poised near an equilibrium miscibility critical point. Critical phenomena explain certain features of the heterogeneity observed in cells and model systems but also go beyond heterogeneity to predict other interesting phenomena, including responses to perturbations in membrane composition.