This paper empirically examines the effects of investment in robots and 4IR digital technologies (specifically big data, Internet of Things, virtual reality, and cybersecurity) on firm employment using a comprehensive and representative firm survey conducted in Italy in 2015 and 2018. We investigate whether these effects are heterogeneous across occupational groups and contractual arrangements. We develop an empirical strategy that allows us to identify the causal effects of the new technologies by combining the predetermined composition of employment at the firm level with the exogenous technological progress in robotics and 4IR digital technologies occurring at the global level, proxied by the technology-related patent stocks at the industry level. This methodology allows us to separately identify the causal effects of robots and of 4IR digital technologies on the overall growth and on the composition of firms' employment as well as, on the firms' training and hiring strategies. Our results tell different stories about the impact of investment in robots and 4IR digital technologies. The impact of robotics investment on firm employment is not statistically significant, but the composition of fixed-term and permanent contracts changes in favour of the former. On the other hand, investment in 4IR digital technologies has a positive effect on firms' employment and their propensity to hire skilled workers in the future. In addition, investment in 4IR digital technologies positively affects the likelihood that firms invest in training (especially IT-related), while it leads to fewer layoffs and lower reliance on temporary workers and intermediation agencies. These results show the coexistence of displacement and reinstatement effects at the firm level. The results are robust to the inclusion of different sets of firm-level controls.