Why was remote work so rare prior to Covid-19's lockdown? One possibility is that working remotely reduces productivity. Another is that remote work attracts unobservably less productive workers. In our setting of call-center workers at a Fortune 500 retailer, two natural experiments reveal positive productivity effects of remote work. When Covid-19 closed down the retailer's on-site call-centers, a difference-in-difference design suggests the transition from on-site to remote work increased the productivity of formerly on-site workers by 8% to 10% relative to their already remote peers. Similarly, when previously on-site workers took up opportunities to go remote in 2018-2019, their productivity rose by 7%. These two natural experiments also reveal negative selection into remote work. While all workers were remote due to Covid-19, those who were hired into remote jobs were 12% less productive than those hired into on-site jobs. Extending remote opportunities to on-site workers similarly attracted less productive workers to on-site jobs. Our model allows us to characterize the counterfactual in which remote workers were not adversely selected. Without adverse selection, the retailer would have hired 57% more remote workers and worker surplus from remote work would have been 32% greater. Given the central role of selection, Covid-19's effect on remote work will persist if the lockdown disproportionately causes more productive workers to be willing to work remotely.