The complexity of the kinematic and dynamic structure of humanoid robots make conventional analytical approaches to control increasingly unsuitable for such systems. Learning techniques offer a possible way to aid controller design if insufficient analytical knowledge is available, and learning approaches seem mandatory when humanoid systems are supposed to become completely autonomous. While recent research in neural networks and statistical learning has focused mostly on learning from finite data sets without stringent constraints on computational efficiency, learning for humanoid robots requires a different setting, characterized by the need for real-time learning performance from an essentially infinite stream of incrementally arriving data. This paper demonstrates how even high-dimensional learning problems of this kind can successfully be dealt with by techniques from nonparametric regression and locally weighted learning. As an example, we describe the application of one of the most advanced of such algorithms, Locally Weighted Projection Regression (LWPR), to the on-line learning of three problems in humanoid motor control: the learning of inverse dynamics models for model-based control, the learning of inverse kinematics of redundant manipulators, and the learning of oculomotor reflexes. All these examples demonstrate fast, i.e., within seconds or minutes, learning convergence with highly accurate final peformance. We conclude that real-time learning for complex motor system like humanoid robots is possible with appropriately tailored algorithms, such that increasingly autonomous robots with massive learning abilities should be achievable in the near future.