Intercepting and avoiding collisions with moving objects are fundamental skills in daily life. Anticipatory behavior is required because of significant delays in transforming sensory information about target and body motion into a timed motor response. The ability to predict the kinematics and kinetics of interception or avoidance hundreds of milliseconds before the event may depend on several different sources of information and on different strategies of sensory-motor coordination. What are exactly the sources of spatio-temporal information and what are the control strategies remain controversial issues. Indeed, these topics have been the battlefield of contrasting views on how the brain interprets visual information to guide movement. Here we attempt a synthetic overview of the vast literature on interception. We discuss in detail the behavioral and neurophysiological aspects of interception of targets falling under gravity, as this topic has received special attention in recent years. We show that visual cues alone are insufficient to predict the time and place of interception or avoidance, and they need to be supplemented by prior knowledge (or internal models) about several features of the dynamic interaction with the moving object.