An algebraic variety is said to be rational if it is birational to projective space. In this talk, westudy the rationality question over the real numbers for a certain class of conic bundle threefolds.The varieties we consider all become rational over the complex numbers, but in general the complex rationality construction need not descend to $ \mathbb{R}$. We discuss rationality obstructions coming from intermediate Jacobian torsors and from the real loci of these varieties.[-]