We introduce a formalism of localization for online learning problems, which, similarly to statistical learning theory, can be used to obtain fast rates. In particular, we introduce local sequential Rademacher complexities and other local measures. Based on the idea of relaxations for deriving algorithms, we provide a template method that takes advantage of localization. Furthermore, we build a general adaptive method that can take advantage of the suboptimality of the observed sequence. We illustrate the utility of the introduced concepts on several problems. Among them is a novel upper bound on regret in terms of classical Rademacher complexity when the data are i.i.d.