The loop space on a topological space is a fundamental construction in topology: it is the space of all continous paths joining a prescribed point to itself. The concatenation of loops endows the loop space with a structure of a group (up to homotopy). Conversely, it is known that any group is in a sense equivalent to a loop space, therefore loop spaces give a way to study groups by looking to some associated topological space.

 In my talk I will explain the so-called ``scanning method'' which gives a combinatorial approach to the study of loop spaces. It shows that interesting loop space can be viewed as some space of configurations of finitely many points in a given manifold. And vice versa, some important configuration spaces turn out to be equivalent to the loops on certain easily constructed spaces. This gives in particular the different viewpoint on some groups like the symmetric group on infinitely many letters or the braid groups. This approach was also used very recently to understand the group of diffeomorphisms of surfaces with very large genus (i.e. the mapping class group) which is a fundamental object in algebraic geometry in the study of bundles by surfaces.