Tilting over commutative rings has for a long time been considered
trivial, for in this case, there are no non-projective finitely
generated tilting modules. But the picture changes completely once we
broaden our horizons to infinitely generated modules. Not only that
approximation theory and category equivalences are still available in
this generality, but a complete classification is possible in many
cases. In this talk, we will start by the relevant general results, and
then deal in detail with the case of commutative noetherian rings.