Three main policy responses to the labour market challenges posed by robotisation and automation have emerged in the research literature. The first is ‘taxing robots’ and using this revenue to introduce a basic income that could offset the negative impacts of replacing humans by robots. The second option highlights the ownership of robots so that taking part in the new source of wealth is possible. The third focuses on strengthening the comparative advantages, the creativity, and the social intelligence of humans that robots will never be able to match. All of these policy responses are supported by economic rationales and research findings, but a systematic review shows that all of them raise further questions and challenges that should be carefully investigated in order to choose the right path. This paper offers a comprehensive overview of these questions. Furthermore, in a broader sense these policy options – redistributing the benefits of technological changes, increasing accesses to the benefits and utilisation of changes, and supporting the individual and institutional adjustment to changes – are relevant to every technological transformation. Hence, the lessons that are drawn from the current discussion of policy options driven by specific technologies, robotization, and automation might serve as a precursor to potential policy responses triggered by other technologies.