Online learning is one of the most important and well-established learning models in machine learning. Generally speaking, the goal of online learning is to make a sequence of accurate predictions “on the fly” when interacting with the environment. Online learning has been extensively studied in recent years, and has also become of great interest to practitioners due to its applicability to large scale applications such as advertisement placement and recommendation systems. In this talk, I will present novel, optimal and adaptive online learning algorithms for three problems. The first problem is online boosting, a theory of boosting the accuracy of any existing online learning algorithms; the second problem is on combining expert advice more efficiently and adaptively when making online predictions; the last part of the talk is about using data sketching techniques to obtain efficient online learning algorithms that make use of second order information and have robust performance against ill-conditioned data.