Interaction control presents opportunities for contact robots physically interacting with their human user, such as assistance targeted to each human user, communication of goals to enable effective teamwork, and task-directed motion resistance in physical training and rehabilitation contexts. Here we review the burgeoning field of interaction control in the control theory and machine learning communities, by analysing the exchange of haptic information between the robot and its human user, and how they share the task effort. We first review the estimation and learning methods to predict the human user intent with the large uncertainty, variability and noise and limited observation of human motion. Based on this motion intent core, typical interaction control strategies are described using a homotopy of shared control parameters. Recent methods of haptic communication and game theory are then presented to consider the co-adaptation of human and robot control and yield versatile interactive control as observed between humans. Finally, the limitations of the presented state of the art are discussed and directions for future research are outlined.