Lipids, cholesterol, and proteins collaborate to organize the plasma membrane of our cells for functional ends, such as signaling and transfer of cargo. New microscopy and imaging techniques are beginning to reveal the structure and dynamics of lipid mixtures on lengthscales well below the diffraction limit, permitting the development and testing of models for cellular organization at the scale of individual signaling events. Chemically detailed molecular simulations reveal an unexpected nanoscale structure in lipid membranes (verified by NMR data), in which cholesterol mediates local hexagonal packing of hydrocarbon chains, which are nonetheless fluid on longer length and timescales. Lipid diffusion is non-Fickian, with subdiffusion observed on timescales that matter for the encounter of signaling partners in the membrane. These results are verified by recent iSCAT single particle tracking experiments, and motivate the development of stochastic subdiffusive models for signaling. Remarkably, subdiffusion offers unexpected advantages for regulating cellular responses from clustered receptors.