The light reactions of photosynthesis in green plants are mediated by four large protein complexes, embedded in the thylakoid membrane of the chloroplast. Photosystem I (PSI) and Photosystem II (PSII) are both organized into large supercomplexes with variable amounts of membrane-bound peripheral antenna complexes. PSI consists of a monomeric core complex with single copies of four different LHCI proteins and has binding sites for additional LHCI and/or LHCII complexes. PSII supercomplexes are dimeric and contain usually two to four copies of trimeric LHCII complexes. These supercomplexes have a further tendency to associate into megacomplexes or into crystalline domains, of which several types have been characterized. Together with the specific lipid composition, the structural features of the main protein complexes of the thylakoid membranes form the main trigger for the segregation of PSII and LHCII from PSI and ATPase into stacked grana membranes. We suggest that the margins, the strongly folded regions of the membranes that connect the grana, are essentially protein-free, and that protein-protein interactions in the lumen also determine the shape of the grana. We also discuss which mechanisms determine the stacking of the thylakoid membranes and how the supramolecular organization of the pigment-protein complexes in the thylakoid membrane and their flexibility may play roles in various regulatory mechanisms of green plant photosynthesis.