It has recently been argued that the elongate necks of sauropod dinosaurs evolved primarily through selection for their use as sexual and dominance signals, and not as an adaptation for accessing a large ‘feeding envelope’ as traditionally thought. Here we explore this idea and show that all six arguments that have been advanced in support of the sexual selection hypothesis are flawed: there is no evidence for sexual dimorphism in the necks of sauropods; neither is there any evidence that they were used in dominance displays; long necks provided significant survival benefits in allowing high browsing and energetically efficient grazing; their fitness cost was likely less than has been assumed; their positive allometry through ontogeny is uninformative given that ontogenetic allometry is common in animals; apparent lack of correlation between neck and leg length across phylogeny is illusory due to over-representation of mamenchisaurids in a previously analysed dataset, and in any case is not informative as the unique morphology of sauropod necks suggests they, rather than legs, may have been cheaper to elongate when evolving increased vertical reach. In no speciose, morphologically varied, long-lived tetrapod clade has sexual selection consistently acted on a single part of the body, and it is unlikely that Sauropoda is the exception to this. In summary, there is no convincing evidence that sexual selection was the primary force driving the evolution of sauropod necks. While a subsidiary role for sexual selection cannot be discounted, the traditional hypothesis that sauropod necks evolved primarily due to the feeding benefits that they conferred is, by comparison, far better supported.