This thesis tackles the fundamental issues of streaming data in different challenging scenarios. First, the confounding problem of class imbalance and concept drift is considered, and a novel and competitive classification framework is proposed to address this challenge. The proposed methodology outperforms the contemporary methods on a number of different datasets. Second, the thesis looks at the problem of dynamic networks, specifically the challenges of link persistence and link prediction. This is the first work to formally cast the problem of link prediction as a class imbalance problem, and it greatly outperforms a number of contemporary and popular methods. The third form of streaming data is in the domain of music. Bach chorales are first uniquely transformed into a feature vector space, and then a sliding window approach is used to generate classifiers for subsequent autonomous music composition.