  A natural class of ideals, almost isometric ideals, of Banach spaces is
defined and studied. The motivation for working with this class of subspaces is
our observation that they inherit diameter 2 properties and the Daugavet
property. Lindenstrauss spaces are known to be the class of Banach spaces that
are ideals in every superspace; we show that being an almost isometric ideal in
every superspace characterizes the class of Gurariy spaces.
