Thylakoids are flattened sacs isolated from other membranes; cristae are attached to the rest of the inner mitochondrial membrane by the crista junction, but the crista lumen is separated from the intermembrane space. The shape of thylakoids and cristae involves membranes with small (5–30 nm) radii of curvature. While the mechanism of curvature is not entirely clear, it seems to be largely a function of Curt proteins in thylakoids and Mitochondrial Organising Site and Crista Organising Centre proteins and oligomeric FOF1 ATP synthase in cristae. A subordinate, or minimal, role is attributable to lipids with areas of their head group area greater (convex leaflet) or smaller (concave leaflet) than the area of the lipid tail; examples of the latter group are monogalactosyldiglyceride in thylakoids and cardiolipin in cristae. The volume per unit area on the lumen side of the membrane is less than that of the chloroplast stroma or cyanobacterial cytosol for thylakoids, and mitochondrial matrix for cristae. A low volume per unit area of thylakoids and cristae means a small lumen width that is the average of wider spaces between lipid parts of the membranes and the narrower gaps dominated by extra-membrane components of transmembrane proteins. These structural constraints have important implications for the movement of the electron carriers plastocyanin and cytochrome c6 (thylakoids) and cytochrome c (cristae) and hence the separation of the membrane-associated electron donors to, and electron acceptors from, these water-soluble electron carriers. The donor/acceptor pairs, are the cytochrome fb6Fenh complex and P700+ in thylakoids, and Complex III and Complex IV of cristae. The other energy flux parallel to the membranes is that of the proton motive force generated by redox-powered H+ pumps into the lumen to the proton motive force use in ATP synthesis by H+ flux from the lumen through the ATP synthase. For both the electron transport and proton motive force movement, concentration differences of reduced and oxidised electron carriers and protonated and deprotonated pH buffers are involved. The need for diffusion along a congested route of these energy transfer agents may limit the separation of sources and sinks parallel to the membranes of thylakoids and cristae.