Infants demonstrate remarkable talents in learning to control their sensory and motor systems. In particular the ability to reach to objects using visual feedback requires overcoming several issues related to coordination, spatial transformations, redundancy, and complex learning spaces. This paper describes a model of longitudinal development that covers the full sequence from blind motor babbling to successful grasping of seen objects. This includes the learning of saccade control, gaze control, torso control, and visually elicited reaching and grasping in 3D space. The paper builds on and extends our prior investigations into the development of gaze control, eye-hand coordination, the use of constraints to shape learning, and a schema memory system for the learning of sensorimotor experience. New contributions include our application of the LWPR algorithm to learn how movements of the torso affect the robot’s representation of space, and the first use of the schema framework to enable grasping and interaction with objects. The results from our integration of these various components into an implementation of longitudinal development on an iCub robot show their ability to generate infant-like development, from a start point with zero coordination up to skilled spatial reaching in less than 3 hours.