In this paper, we provide new estimates of the impact of unions on non-union wage setting. We allow the presence of unions to affect non-union wages both through the typically discussed channel of non-union firms emulating union wages in order to fend off the threat of unionisation and through a bargaining channel in which non-union workers use the presence of union jobs as part of their outside option. We specify these channels in a search and bargaining framework that includes union formation and the possibility of non-union firm responses to the threat of unionisation. Our results indicate an important role played by union wage spillovers in lowering wages over the 1980-2010 period. We find that de-unionisation can account for nearly a third of the decline in the mean hourly wage between 1980 and 2010 in the US, with half of that effect being due to spillovers. Both the traditional threat and bargaining channels are operational, with the bargaining channel being more important.