This thesis explores the application of ensemble methods to sequential learning tasks. The focus is on the development and the critical examination of new methods or novel applications of existing methods, with emphasis on supervised and reinforcement learning problems. In both types of problems, even after having observed a certain amount of data, we are often faced with uncertainty as to which hypothesis is correct among all the possible ones. However, in many methods for both supervised and for reinforcement learning problems this uncertainty is ignored, in the sense that there is a single solution selected out of the whole of the hypothesis space. Apart from the classical solution of analytical Bayesian formulations, ensemble methods offer an alternative approach to representing this uncertainty. This is done simply through maintaining a set of alternative hypotheses. The sequential supervised problem considered is that of automatic speech recognition using hidden Markov models. The application of ensemble methods to the problem represents a challenge in itself, since most such methods can not be readily adapted to sequential learning tasks. This thesis proposes a number of different approaches for applying ensemble methods to speech recognition and develops methods for effective training of phonetic mixtures with or without access to phonetic alignment data. Furthermore, the notion of expected loss is introduced for integrating probabilistic models with the boosting approach. In some cases substantial improvements over the baseline system are obtained. In reinforcement learning problems the goal is to act in such a way as to maximise future reward in a given environment. In such problems uncertainty becomes important since neither the environment nor the distribution of rewards that result from each action are known. This thesis presents novel algorithms for acting nearly optimally under uncertainty based on theoretical considerations. Some ensemble-based representations of uncertainty (including a fully Bayesian model) are developed and tested on a few simple tasks resulting in performance comparable with the state of the art. The thesis also draws some parallels between a proposed representation of uncertainty based on gradient-estimates and on"prioritised sweeping" and between the application of reinforcement learning to controlling an ensemble of classifiers and classical supervised ensemble learning methods.