Soft robots (SRs) represent one of the most significant recent evolutions in robotics. Designed to embody safe and natural behaviors, they rely on compliant physical structures purposefully designed to embody desirable and sometimes variable impedance characteristics. This article discusses the problem of controlling SRs. We start by observing that most of the standard methods of robotic control—e.g., high-gain robust control, feedback linearization, backstepping, and active impedance control—effectively fight against or even completely cancel the physical dynamics of the system, replacing them with a desired model. This defeats the purpose of introducing physical compliance. After all, what is the point of building soft actuators if we then make them stiff by control? An alternative to such approaches can be conceived by observing humans, who can obtain good motion accuracy and repeatability while maintaining the intrinsic softness of their bodies. In this article, we show that an anticipative model of human motor control, using a feedforward action combined with low-gain feedback, can be used to achieve human-like behavior. We present an implementation of such an idea that uses iterative learning control. Finally, we present the experimental results of the application of such learned anticipative control to a physically compliant robot. The control application achieves the desired behavior much better than a classical feedback controller used for comparison.