Electronic devices may include assemblies of structures such as electronic device assemblies connected using light-cured liquid adhesive such as ultraviolet-light-cured adhesive. Light guide structures may be mounted in the assemblies. During manufacture of an electronic device, ultraviolet light may be injected into a light guide structure to cure the light-cured liquid adhesive. A light guide structure may include portions that prevent escape of ultraviolet light and portions that allow ultraviolet light to escape into the light-cured liquid adhesive. Light guide structures may include masked portions, rigid support members, and one or more openings. Openings in a light guide structure may allow the light-cured liquid adhesive to be injected into an assembly through the openings. An adhesive applicator may be used to apply the adhesive to portions of the assembly. An external light source may be used to inject light that cures the adhesive into the light guide structures.