We analyse the moderating effect of trade unions on industrial employment and unemployment in countries facing exposure to industrial robots. Applying random effects within-between regression to a pseudo-panel of observations from 28 advanced democracies over 1998-2019, we find that stronger trade unions in a country are associated with a greater decline in the industry sector employment of young and low-educated workers. We also show that the unemployment rates for low-educated workers remain constant in strongly unionised countries with increasing exposure to robots, whereas in weakly unionised countries, low-educated unemployment declines with robot exposure but from a higher starting point. Our results point to unions exacerbating the insider-outsider effects of technological change within the industrial sector, which however is not fully passed on to unemployment.