The notion of the localized Lascar-Galois group GalL(p) of a type p appeared recently in the context of model-theoretic homology groups, and was also used by Krupinski, Newelski, and Simon in the context of topological dynamics. After a brief introduction of the context, we will discuss some basic properties of localized Lascar-Galois groups. Then, we will focus on the question about how far GalL(tp(acl(a))) can be from GalL(tp(a)). This is a joint work with B. Kim, A. Kolesnikov and J. Lee.