It is generally assumed that already in the next decade, the use of labour-saving robots with implemented artificial intelligence will lead to a dramatic transition of the workforce in almost all sectors of production and services. The ensuing loss of jobs that have traditionally been performed by a human employees is likely to result at least temporarily in reduced wage tax and payroll tax revenues, increasing income inequality and a disruption of the labour market. Against this backdrop, the idea of taxing the use of robots that replace human workforce, or even taxing the robots themselves, has emerged in politics and scholarly writings. Several justifications have been brought forward by its proponents: the robot tax has been regarded, respectively, as a corollary to a soon-to-be-expected concession of civil law personhood to robots, as a tax on imputed income earned by means of the robot, as an equalisation levy to restore the level playing field regarding the taxation of robots and of human workers, as an instrument for economically efficient wage compression between winners and losers of automation among the human workforce, or as a corrective tax to slow down the disruption of the labour market. This paper argues that upon a closer look, the case for taxing robots or their use is relatively weak, though, except when specific conditions are met. There is currently no compelling argument to make robots themselves taxable persons, neither for the purposes of income taxation nor for the purposes of indirect taxes on consumption expenditure. Moreover, significant objections can also be raised regarding suggestions to tax the use of robots. Some of the concepts advanced in literature rely on presumptions that are either conceptually flawed or lack credible empirical support. Other proposals have their merits, but when weighing in on their potential benefits, policymakers will also have to take into account that any tax on robots is liable to result in distortions, complexities, and reduced growth. Besides, proponents of a robot tax tend to underestimate how capital mobility and international tax competition could easily undermine the respective objective of such a tax. As a Pigouvian tax, a robot tax will therefore likely have a very limited field of reasonable application. Regarding income redistribution and revenue raising objectives, the taxation of robots should only be considered as a measure of last resort, and in any event a provisional one. Where politically feasible, priority should instead be given to intensified efforts to tax the return on capital investments and on profits in general, including an adequate taxation of ultimate shareholders. In any event, increasing automation should have implications for the international allocation of taxing rights.