Direct air capture and storage is a technological solution to removing CO2 from our atmosphere that is deemed necessary to reach climate targets. However, huge question marks remain over the current and future costs. Here, we show the cost of DACS, for four example technologies, of plants built today before we project these costs into the future using technological learning theory. We exhibit that the costs of the first plants will be higher than many figures quoted today, but long-term, this can reduce to $80-600 t-CO2-1 at the Gt-CO2 year-1 technology scale. We also show that intelligent deployment via siting and energy source selection is critical and can save a few thousand dollars per t-CO2-1 for some technologies. Finally, we explore which policies can help create a market, accelerate scale-up, and reduce the long-term costs of direct air capture as a potentially vast future industry.