Refiection is an important concept in category theory. Some constructions in  algebra, analysis, and topology  can be viewed as reflections in a nature way. In this talk, we will give an introduction to  reflections in  some concrete categories and  pay more attention  to  reflections in  the category of topological groups. Then we introduce  some recent work done by professor Tkachenko which inspires our research. Finally we will discuss  our  work on the τ-precompact Hausdorff group reflection of topological groups, this is a joint work  with professor Wei He.