Perception and action are fundamental processes that characterize our life and our possibility to modify the world around us. Several pieces of evidence have shown an intimate and reciprocal interaction between perception and action, leading us to believe that these processes rely on a common set of representations. The present review focuses on one particular aspect of this interaction: the influence of action on perception from a motor effector perspective during two phases, action planning and the phase following execution of the action. The movements performed by eyes, hands, and legs have a different impact on object and space perception; studies that use different approaches and paradigms have formed an interesting general picture that demonstrates the existence of an action effect on perception, before as well as after its execution. Although the mechanisms of this effect are still being debated, different studies have demonstrated that most of the time this effect pragmatically shapes and primes perception of relevant features of the object or environment which calls for action; at other times it improves our perception through motor experience and learning. Finally, a future perspective is provided, in which we suggest that these mechanisms can be exploited to increase trust in artificial intelligence systems that are able to interact with humans.