Automated mobility has always conveyed fantasies about its ability to meet future mobility challenges. If research is still debating the when, where and how of this mobility disruption, there seems to be a consensus on its advent. Meanwhile, the investigation of the demand for this mobility is of critical importance. Stated preference surveys are a common and powerful tool to foresee this demand. This paper tackles the question of the acceptance of shared autonomous vehicles (SAVs) by reviewing most significant published papers on travel demand surveys for SAVs. The paper updates and complements previous literature reviews.