For threefolds over the complex numbers, much is understood about the rationality problem, i.e. the property of being birational to projective space. However, much less is known over fields that are not algebraically closed. For example, a threefold defined over the real numbers could become rational after base changing to C, but in general, the complex rationality construction may not descend to R. In this talk, we study this question for real threefolds with a conic bundle structure. This talk is based on joint work with S. Frei, S. Sankar, B. Viray, and I. Vogt, and joint work with M. Ji.