  This survey reviews some facts about nonnegativity conditions on the
curvature tensor of a Riemannian manifold which are preserved by the action of
the Ricci flow. The text focuses on two main points. First we describe the
known examples of preserved curvature con-ditions and how they have been used
to derive geometric results, in particular sphere theorems. We then describe
some recent results which give restrictions on general preserved conditions.
The paper ends with some open questions on these matters. The Ricci flow is the
following evolution equation:
