  Conway's field No of surreal numbers comes both with a natural total order
and an additional "simplicity relation" which is also a partial order.
Considering No as a doubly ordered structure for these two orderings, an
isomorphic copy of No into itself is called a surreal substructure. It turns
out that many natural subclasses of No are actually of this type. In this
paper, we study various constructions that give rise to surreal substructures
and analyze important examples in greater detail.
