Sensorimotor behaviors often rely on model-driven control. In vertebrates, such as primates, even simple reaching gestures are constructed through the use of internal models of the body (forward and inverse models) and the world. How such models are implemented at the neuronal level remains a major unsolved question in systems neuroscience. Here I explore this question in a novel context, relying on the sophisticated sensorimotor behavior and compact neuroanatomy of insects to both complement and contrast the extensive work done in vertebrates. Using dragonfly prey capture as a model system, I will discuss four key results. First, high resolution three dimensional free flight kinematic data demonstrate that interception guidance steering is based inverse models that implement a predictive flight path. Second, in-flight steering of the head relies on forward and inverse models to stabilize the prey image against self-motion and prey-motion. Third, both body and head steering use internal states as well as visual feedback and can proceed with their kinematics in the absence of vision based on memory alone. Finally, I will show that the underlying neuroanatomy is consistent with this behavior being driven by a series of parallel internal models, and I will discuss the anatomical elements and connectivity that we hypothesize form building blocks of the visually-driven portions of the forward and inverse models. If correct, these data imply a neuronal implementation of internal models substantially more distributed and implicit than the discretized and explicit representations we observe at the level of behavior.