A nonexpansive self-mapping of a bounded, closed and convex subset of a Banach space is called extremal if it does not have a representation as a non-trivial convex combination of nonexpansive mappings. We show that on the unit ball of many classical Banach spaces surjective isometries are extremal among nonexpansive mappings. We also show that the typical, in the sense of Baire category, nonexpansive mapping is close to be extremal. This is joint work with Katriin Pirk and Michael Dymond.