A major challenge in robotics is the ability to learn, from novel experiences, new behavior that is useful for achieving new goals and skills. Autonomous systems must be able to learn solely through the environment, thus ruling out a priori task knowledge, tuning, extensive training, or other forms of pre-programming. Learning must also be cumulative and incremental, as complex skills are built on top of primitive skills. Additionally, it must be driven by intrinsic motivation because formative experience is gained through autonomous activity, even in the absence of extrinsic goals or tasks. This paper presents an approach to these issues through robotic implementations inspired by the learning behavior of human infants. We describe an approach to developmental learning and present results from a demonstration of longitudinal development on an iCub humanoid robot. The results cover the rapid emergence of staged behavior, the role of constraints in development, the effect of bootstrapping between stages, and the use of a schema memory of experiential fragments in learning new skills. The context is a longitudinal experiment in which the robot advanced from uncontrolled motor babbling to skilled hand/eye integrated reaching and basic manipulation of objects. This approach offers promise for further fast and effective sensory-motor learning techniques for robotic learning.