We present SurfaceLink, a system where users can make natural surface gestures to control association and information transfer among a set of devices that are placed on a mutually shared surface (e.g., a table). SurfaceLink uses a combination of on-device accelerometers, vibration motors, speakers and microphones (and, optionally, an off-device contact microphone for greater sensitivity) to sense gestures performed on the shared surface. In a controlled evaluation with 10 participants, SurfaceLink detected the presence of devices on the same surface with 97.7% accuracy, their relative arrangement with 89.4% accuracy, and various single- and multi-touch surface gestures with an average accuracy of 90.3%. A usability analysis showed that SurfaceLink has advantages over current multi-device interaction techniques in a number of situations.