In order to realize safe, effective and human-like physical interaction between a robot and a human, it is crucial to first understand how humans interact with each other. Pioneering work in physical human-human interaction (pHHI) report small interaction forces below 20 N, and sometimes even below 1 N. This is too small to provide any mechanical support or substantial power transfer. Instead, it is speculated that the role of small interaction forces is the information transfer about ongoing interaction. It can be very effective to a point where even neurologically impaired patients could improve their motor performance through small forces. What, then, is encoded in interaction forces specifically? In this talk, I will present two case studies of physical human-robot interaction (pHRI), where the force exchange was shown to be related to both subjective and objective measures of the quality of the interaction. In particular, I will show that the interaction force that encodes human movement kinematics was successful in improving human balance. These findings provide rich implications on the design of robots and wearable devices for assisting human movement through physical contact.