Prompted by rising income inequality (in short, inequality) in advanced economies, a rapidly growing number of studies across various fields and disciplines of social science have, since the 1990s, sought to find out how innovation (as the main engine of economic progress) affects the distribution of income in modern-day capitalist societies. Using the systematic literature review method, this paper provides the first critical review of 166 studies on innovation and inequality published in 114 journals in the last three decades (1990-2019). It is shown that while the great majority of studies under review concur that innovation induces inequality, this finding is subject to the disciplinary origins of research (e.g., development studies, economics, geography, innovation studies etc.) and the country under investigation. Furthermore, guided by an original causally-holistic analytical framework, the analysis demonstrates that the relationship between innovation and inequality is significantly more causally complex than the most popular theoretical perspective (i.e., skill-biased technological change account) has let us believe; in particular, it is subject to five causal scenarios and a range of explanatory factors (i.e., skill premiums, technological unemployment, international trade, declining union membership, spatial aspects, changing employment conditions, policy, horizontal inequalities, sectoral composition and types of innovation). The paper ends by discussing findings, policy implications and knowledge gaps, one of which concerns the following under-researched question: How, and under what conditions do publicly-funded innovation policies reduce (or increase) inequality?