ABSTRACT
This chapter reports on some new results and conjectures about the rationality of conic bundles. It discusses rationality criteria for 3-dimensional conic bundles. Every conic bundle is birationally equivalent to a standard one. It presents the conjectures of V. A. Iskovskikh. V. V. Shokurov has conjectured that (*) holds for every conic bundle and every S. Iskovskikh reports that Gizatullin has found that Millevoi’s counterexample is wrong, but no proof of this statement has yet appeared. It may be noted that it is not known whether all conic bundles (even with base P2) are unirational or not. It is conjectured that the answer to this question is negative.
