The article is devoted to the transformation of tax systems in the age of digitalization of economy. As the main challenge the authors suggest the issue of technological unemployment and the increasing income inequality explained by the skill-based divide. The authors identify different possible outcomes for tax systems of more and less developed states. The authors analyze the prospects for multilateral tax cooperation as economic policy tool targeted to slow down the technological unemployment and growing inequality (both between and inside countries). After examining the economic interests of developed and developing states for concluding treaties authors suggest that cooperation scenario is unlikely to be feasible today, putting the fiscal systems of the poorest states in a highly vulnerable position. The final part of the article is devoted to the issues of adjusting the Russian tax system to the challenges of the digitalized economy.