Linker of nucleoskeleton and cytoskeleton (LINC) complexes couple the nucleus to the cytoplasm. Here, Sosa et al. describe how their components, SUN and KASH proteins, interact to build strong connections through the nuclear envelope. SUN proteins, which span the inner nuclear membrane, trimerize through their luminal SUN domains and the adjacent coiled-coil domains. The authors show that trimeric SUN domains can bind three KASH domains, which are found on the luminal end of the outer nuclear membrane-spanning KASH proteins. SUN–KASH binding is stabilized by extended SUN–KASH domain interactions and a disulphide bond. The resolved structures suggest that SUN trimerization may enable higher-order organization of SUN–KASH complexes to sustain the strong forces that are exerted between the nucleus and the cytoplasm.