Inequality is one of the main challenges posed by the proliferation of artificial intelligence (AI) and other forms of worker-replacing technological progress. This paper provides a taxonomy of the associated economic issues: First, we discuss the general conditions under which new technologies such as AI may lead to a Pareto improvement. Secondly, we delineate the two main channels through which inequality is affected – the surplus arising to innovators and redistributions arising from factor price changes. Third, we provide several simple economic models to describe how policy can counter these effects, even in the case of a “singularity” where machines come to dominate human labor. Under plausible conditions, non-distortionary taxation can be levied to compensate those who otherwise might lose. Fourth, we describe the two main channels through which technological progress may lead to technological unemployment – via efficiency wage effects and as a transitional phenomenon. Lastly, we speculate on how technologies to create super-human levels of intelligence may affect inequality and on how to save humanity from the Malthusian destiny that may ensue.