In this talk, I will focus on some first examples of certain higher structures and their impact in geometry. My higher structures here are the $2$-group(oid) structures. They also have their infinitesimal versions, namely the higher Lie algebra(oid)s. In this view point, for example, a group (resp. a higher groupoid) is viewed as a space with a certain higher structure (resp. an even higher structure). The advantages of this new viewpoint will be explained in the second part of my talk.