| The Zilber Pink conjectures on unlikely intersections predict the behaviour of subvarieties of families of (semi)abelian varieties or of Shimura varieties when intersected with special subvarieties and generalises many well-known conjectures/results like Manin-Mumford, Mordell-Lang and André-Oort. After introducing the problem and giving different versions of the conjectures I will talk about recent results for curves in families of abelian varieties (joint work with L. Capuano) and in semiabelian varieties (joint work with H. Schmidt). All of these results have been proved for varieties over the algebraic numbers. In joint work in progress with G. Dill we are extending some of the known results to varieties over fields of characteristic 0. |