The process of oxygenic photosynthesis enabled and still sustains aerobic life on Earth. The most elaborate form of the apparatus that carries out the primary steps of this vital process is the one present in higher plants. Here, we review the overall composition and supramolecular organization of this apparatus, as well as the complex architecture of the lamellar system within which it is harbored. Along the way, we refer to the genetic, biochemical, spectroscopic and, in particular, microscopic studies that have been employed to elucidate the structure and working of this remarkable molecular energy conversion device. As an example of the highly dynamic nature of the apparatus, we discuss the molecular and structural events that enable it to maintain high photosynthetic yields under fluctuating light conditions. We conclude the review with a summary of the hypotheses made over the years about the driving forces that underlie the partition of the lamellar system of higher plants and certain green algae into appressed and non-appressed membrane domains and the segregation of the photosynthetic protein complexes within these domains.