In this talk, we will introduce  (strict) higher categories and (strict)  higher groupoids. We will present Street nerve which associates to every  higher groupoid, a Kan complex. We will give an overview of the proof of the non-existence of a  higher groupoids whose nerve has the homotopy type of the 2-sphere.

If time permits, we will present a generalization of the Street nerve which associates to any (well  marked) higher category  a complicial set.