In this work, we are primarily concerned with robotic systems that learn online and continuously from multi-variate data-streams. Our first contribution is a new recursive kernel, which we have integrated into a sparse Gaussian Process to yield the Spatio-Temporal Online Recursive Kernel Gaussian Process (STORK-GP). This algorithm iteratively learns from time-series, providing both predictions and uncertainty estimates. Experiments on benchmarks demonstrate that our method achieves high accuracies relative to state-of-the-art methods. Second, we contribute an online tactile classifier which uses an array of STORK-GP experts. In contrast to existing work, our classifier is capable of learning new objects as they are presented, improving itself over time. We show that our approach yields results comparable to highly-optimised offline classification methods. Moreover, we conducted experiments with human subjects in a similar online setting with true-label feedback and present the insights gained.