Precise models of technical systems and the task to be accomplished can be crucial in technical applications. In robot tracking control, only a well-estimated inverse dynamics model results in both high accuracy and compliant, low-gain control. For complex robots such as humanoids or lightweight robot arms, it is often hard to analytically model the system sufficiently well and, thus, modern regression methods can offer a viable alternative. Current regression methods such as Gaussian process regression or locally weighted projection regression either have high computational cost or are not straightforward to use (respectively). Hence, task-appropriate real-time methods are needed in order to achieve high performance. This project uses the large body of insights from modern online learning methods and applied them in the context of robot learning. Particularly, we focussed on three novel problems that have not yet been tackled in the literature. The first two problems are in the learning of inverse dynamics domain: current methods largely neglect the existence of input noise and only focus on output noise. We considered both sources of noise together. This may have far reaching consequences: the input noise only exists in training data while in the recall or control case it no longer occurs. Secondly, we studied the bias originating from the active data generation that is part of the online learning problem. Our intention was to build on recent advances in online learning algorithms, such as the confidence-weighted algorithm (CW) and the adaptive-regularization-algorithm (AROW), and design, analyze and experiment new techniques and method to cope with the above challenges. Success will allow us to build better robot controllers for smooth and delicate robot dynamics.