In this thesis, we study Online Convex Optimization algorithms that exploit predictive and/or dynamical information about a problem instance. These features are inspired by recent developments in the Online Mirror Decent literature. When the Player's performance is compared with the best fixed decision in hindsight, we show that it is possible to achieve constant regret bounds under perfect gradient predictions and optimal minimax bounds in the worst-case, generalizing previous results from the literature. For dynamic environments, we propose a new algorithm, and show that it achieves dynamic regret bounds that exploit both gradient predictions and knowledge about the dynamics of the action sequence that the Player's performance is being compared with. We present results for both convex and strongly convex costs. Finally, we provide numerical experiments that corroborate our theoretical results.