Multiple electronic devices may be used together in a system. The electronic devices may use sensor measurements and other information to detect when an edge of a first electronic device is adjacent to an edge of a second electronic device. In response to detection of adjacency between the edges of the first and second devices, the devices may transition from an independent operating mode in which each device operates separately to a joint operating mode in which resources of the devices are shared. In the joint operating mode, images may extend across displays in the devices, speakers in the devices may be used to play different channels of an audio track, cameras and other sensors may be used in cooperation with each other, and other resources may be shared. Magnetic components may hold devices together in a variety of orientations.