The rationality problem for conic bundles

@article{Prokhorov2018TheRP,
  title={The rationality problem for conic bundles},
  author={Yuri G. Prokhorov},
  journal={Russian Mathematical Surveys},
  year={2018},
  volume={73},
  pages={375 - 456}
}
This expository paper is concerned with the rationality problem for three-dimensional algebraic varieties with a conic bundle structure. The main methods of this theory are discussed, proofs of certain principal results are sketched, and some recent achievements are presented. Many open problems are also stated. Bibliography: 209 titles. 

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