Plasmodesmata (PD) are plant-specific intercellular nanopores defined by specialised domains of the plasma membrane (PM) and the endoplasmic reticulum (ER), both of which contain unique proteins, and probably different lipid compositions than the surrounding bulk membranes. The PD membranes form concentric tubules with a minimal outer diameter of only 50 nm, and the central ER strand constricted to ~10-15 nm, representing one of the narrowest stable membrane tubules in nature. This unique membrane architecture poses many biophysical, structural and functional questions. PM continuity across PD raises the question as to how a locally confined membrane site is established and maintained at PD. There is increasing evidence that the PM within PD may be enriched in membrane 'rafts' or TET web domains. Lipid rafts often function as signalling platforms, in line with the emerging view of PD as central players in plant defense responses. Lipid-lipid immiscibility could also provide a mechanism for membrane sub- compartmentalisation at PD. Intricate connections of the PM to the wall and the underlying cytoskeleton and ER may anchor the specialised domains locally. The ER within PD is even more strongly modified. Its extreme curvature suggests that it is stabilised by densely packed proteins, potentially members of the reticulon family that tubulate the cortical ER. The diameter of the constricted ER within PD is similar to membrane stalks in dynamin-mediated membrane fission during endocytosis and may need to be stabilised against spontaneous rupture. The function of this extreme membrane constriction, and the reasons why the ER is connected between plant cells remain unknown. Whilst the technically challenging search for the protein components of PD is ongoing, there has been significant recent progress in research on biological membranes that could benefit our understanding of PD function. With this Research Topic, we therefore aim to bring together researchers in the PD field and those in related areas, such as membrane biophysics, membrane composition and fluidity, protein-lipid interactions, lateral membrane heterogeneity, lipid rafts, membrane curvature, and membrane fusion/fission.